# Question Answers

Part 1

Question 1 of 23

The chi-square goodness-of-fit test can be used to test for:

A.difference between population variances

B.significance of sample statistics

C.difference between population means

D.normality

Question 2 of 23

A company operates four machines during three shifts each day. From production records, the data in the table below were collected. At the .05 level of significance test to determine if the number of breakdowns is independent of the shift.

A.The number of breakdowns is dependent on the shift, because the test value 11.649 is less than the critical value of 12.592.

B.The claim that the number of breakdowns is independent of the shift cannot be rejected, because the test value 11.649 is less than the critical value of 12.592.

C.The number of breakdowns is dependent on the shift, because the p-value is .07.

D.The number of breakdowns is independent of the shift, because the test value 12.592 is greater than the critical value of 11.649.

Part 2

Question 3

Correlation is a summary measure that indicates:

A.a curved relationship among the variables

B.the strength of the linear relationship between pairs of variables

C.the magnitude of difference between two variables

D.the rate of change in Y for a one unit change in X

Question 4

In regression analysis, the variable we are trying to explain or predict is called the

A.dependent variable

B.independent variable

C.regression variable

D.residual variable

Question 5

If an estimated regression line has a Y-intercept of –7.5 and a slope of 2.5, then when X = 3, the actual value of Y is:

A.10

B.5

C.unknown

D.0

Part 3

Question 6

Q-Mart is interested in comparing its male and female customers. Q-Mart would like to know if the amount of money spent by its female charge customers differs, on average, from the amount spent by its male charge customers.

To answer this question, an analyst collected random samples of 25 female customers and 22 male customers. Based on these samples, on average, the 25 women charge customers spent $102.23 and the 22 men charge customers spent $86.46. Moreover, the sample standard deviation of the amount charged by the 25 women was $93.393, and the sample standard deviation of the amount charged by the 22 men was $59.695.

Using the procedure advocated by Bluman, at the 10% level of significance, is there sufficient evidence for Q-Mart to conclude that, on average, the amount spent by women charge customers differs from the amount spent by men charge customers.

A.No, the test value does not exceed the critical value.

B.No, the p-value of this test is less than 0.10.

C.Yes, the p-value of this test is greater than 0.10

D.Yes, the test value does not exceed the critical value

Question 7

Multiple myeloma or blood plasma cancer is characterized by increased blood vessel formulation in the bone marrow that is a prognostic factor in survival. One treatment approach used for multiple myeloma is stem cell transplantation with the patient’s own stem cells. The following data represent the bone marrow microvessel density for a sample of 7 patients who had a complete response to a stem cell transplant as measured by blood and urine tests. Two measurements were taken: the first immediately prior to the stem cell transplant, and the second at the time of the complete response.

Patient 1 2 3 4 5 6 7

Before 158 189 202 353 416 426 441

After 284 214 101 227 290 176 290

Suppose you wanted to conduct a test of hypothesis to determine if there is sufficient evidence to conclude that the mean bone marrow microvessel density is higher before the stem cell transplant than after the stem cell transplant? What is the p-value associated with the test of hypothesis you would conduct?

A.p = .114986

B.p = .942597

C.p = .885014

D.p = .057493

Question 8

Results from previous studies showed 79% of all high school seniors from a certain city plan to attend college after graduation. A random sample of 200 high school seniors from this city reveals that 162 plan to attend college. Does this indicate that the percentage has increased from that of previous studies? Test at the 5% level of significance.

Compute the z or t value of the sample test statistic.

A.z = 0.69

B.t = 1.645

C.z = 1.96

D.z = 0.62

Question 9

In an article appearing in Today’s Health a writer states that the average number of calories in a serving of popcorn is 75. To determine if the average number of calories in a serving of popcorn is different from 75, a nutritionist selected a random sample of 20 servings of popcorn and computed the sample mean number of calories per serving to be 78 with a sample standard deviation of 7.

State the null and alternative hypotheses.

A.H0: = 75, H1: 75

B.H0: 75, H1: 75

C.H0: 75, H1: < 75

D.H0: = 75, H1: ≠ 75

Question 10

In an article appearing in Today’s Health a writer states that the average number of calories in a serving of popcorn is 75. To determine if the average number of calories in a serving of popcorn is different from 75, a nutritionist selected a random sample of 20 servings of popcorn and computed the sample mean number of calories per serving to be 78 with a sample standard deviation of 7.

Compute the z or t value of the sample test statistic.

A.t = 1.916

B.t = -1.916

C.z = 1.645

D.z = 1.916

Part 5

Question 11

Confidence intervals are a function of which of the following three things?

A.The sample, the variable of interest, and the degrees of freedom

B.The data in the sample, the confidence level, and the sample size

C.The population, the sample, and the standard deviation

D.The sampling distribution, the confidence level, and the degrees of freedom

Question 12

In order to be accepted into a top university, applicants must score within the top 5% on the SAT exam. Given that SAT test scores are normally distributed with a mean of 1000 and a standard deviation of 200, what is the lowest possible score a student needs to qualify for acceptance into the university?

A.1330

B.1400

C.1250

D.1100

Part 6

Question 13

The continuous distribution characterized by a symmetric, bell-shaped curve is the:

A.binomial distribution

B.Poisson distribution

C.normal distribution

D.exponential distribution

Part 7

Question 14

A pet supplier has a stock of parakeets of which 10% are blue parakeets. A pet store orders 3 parakeets from this supplier. If the supplier selects the parakeets at random, what is the chance that the pet store gets exactly one blue parakeet?

A.0.081

B.0.243

C.0.027

D.0.003

Part 8

Question 15

If 25 tickets are sold and 2 prizes are to be awarded, find the probability that one person will win both prizes if that person buys exactly 2 tickets.

A.1/2300

B.1/300

C.1/700

D.1/600

Part 9

Question 16 3.0 Points

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

Staples, a chain of large office supply stores, sells a line of desktop and laptop computers. Company executives want to know whether the demands for these two types of computers are dependent on one another. Each day's demand for each type of computers is categorized as Low, Medium-Low, Medium-High, or High. The data shown in the table below is based on 200 days of operation. Based on these data, can Staples conclude that demands for these two types of computers are independent? Test at the 5% level of significance.

desktops

low med-low med-high high

low 3 14 14 4 35

laptops med-low 6 18 17 22 63

med-high 13 16 11 16 56

high 8 14 15 9 46

30 62 57 51 200

What is the test value for this hypothesis test?

Answer: Round your answer to two decimal places.

What is the critical value for this hypothesis test?

Answer: Round your answer to two decimal places.

What is the conclusion for this hypothesis test? Choose one.

1. At the .05 level of significance, Staples can conclude that demands for these two types of computers are independent.

2. At the .05 level of significance, Staples can conclude that demands for these two types of computers are dependent.

Answer: Enter only a 1 or 2 for your answer.

Part 10

Question 17

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

The marketing manager of a large supermarket chain would like to determine the effect of shelf space (in feet) on the weekly sales of international food (in hundreds of dollars). A random sample of 12 equal –sized stores is selected, with the following results:

Store Shelf Space(X) Weekly Sales(Y)

1 10 2.0

2 10 2.6

3 10 1.8

4 15 2.3

5 15 2.8

6 15 3.0

7 20 2.7

8 20 3.1

9 20 3.2

10 25 3.0

11 25 3.3

12 25 3.5

Find the equation of the regression line for these data. What is the value of the coefficient of determination? Place your answer, rounded to 3 decimal places, in the blank. Do not use a dollar sign. For example, 0.345 would be a legitimate entry.

Part 11

Question 18

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

Are America's top chief executive officers (CEOs) really worth all that money? One way to answer this question is to look at the annual company percentage increase in revenue versus the CEO's annual percentage salary increase in that same company. Suppose that a random sample of companies yielded the following data:

percent change for corporation 15 12 3 12 28 6 8 2

percent change for CEO 6 17 -4 12 32 -1 7 2

Do these data indicate that the population mean percentage increase in corporate revenue is greater than the population mean percentage increase in CEO salary? Use a 5% level of significance. What is the critical value that you would use to conduct this test of hypothesis? Place your answer, rounded to 3 decimal places, in the blank. For example, 2.345 would be a legitimate entry.

Part 12

Question 19

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

Scores on a mathematics examination appear to follow a normal distribution with mean of 65 and standard deviation of 15. The instructor wishes to give a grade of “C” to students scoring between the 60th and 70th percentiles on the exam.

What score represents the 70th percentile score on the mathematics exam? Place your answer in the blank, rounded to a whole number. For example, 62 would be a legitimate entry.

Part 13

Question 20

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

The manufacturer of a new compact car claims the miles per gallon (mpg) for the gasoline consumption is mound-shaped and symmetric with a mean of 25.9 mpg and a standard deviation of 9.5 mpg. If 30 such cars are tested, what is the probability the average mpg achieved by these 30 cars will be greater than 28?

Answer: Round your answer to 4 decimal places as necessary. For example, 0.1357 would be a legitimate entry.

Part 14

Question 21

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

Find the mean of the probability distribution:

X 0 1 2 3 4

P(X) 0.12 0.16 0.24 0.30 0.18

Round your answer to two decimal place as necessary. For example, 4.56 would be a legitimate entry.

Mean =

Part 15

Question 22

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

The ABC battery company claims that their batteries last at least 100 hours, on average. Your experience with their batteries has been somewhat different, so you decide to conduct a test to see if the company's claim is true. You believe that the mean life is actually less than the 100 hours the company claims. You decide to collect data on the average battery life (in hours) of a random sample of n = 20 batteries. Some of the information related to the hypothesis test is presented below.

Test of H0: 100 versus H1: 100

Sample mean 98.5

Std error of mean 0.777

Assuming the life length of batteries is normally distributed, if you wish to conduct this test using a .05 level of significance, what is the critical value that you should use? Place your answer, rounded to 3 decimal places in the blank. For example, -1.234 would be a legitimate entry.

Part 16

Question 23

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

An ice cream vendor sells three flavors: chocolate, strawberry, and vanilla. Forty five percent of the sales are chocolate, while 30% are strawberry, with the rest vanilla flavored. Sales are by the cone or the cup. The percentages of cones sales for chocolate, strawberry, and vanilla, are 75%, 60%, and 40%, respectively. For a randomly selected sale, define the following events:

= chocolate chosen

= strawberry chosen

= vanilla chosen

= ice cream on a cone

ice cream in a cup

Find the probability that the ice cream was chocolate flavor, given that it was sold in a cup. Place your answer, rounded to 4 decimal places, in the blank. For exampe, 0.3456 would be a legitimate entry.

Question 1 of 23

The chi-square goodness-of-fit test can be used to test for:

A.difference between population variances

B.significance of sample statistics

C.difference between population means

D.normality

Question 2 of 23

A company operates four machines during three shifts each day. From production records, the data in the table below were collected. At the .05 level of significance test to determine if the number of breakdowns is independent of the shift.

A.The number of breakdowns is dependent on the shift, because the test value 11.649 is less than the critical value of 12.592.

B.The claim that the number of breakdowns is independent of the shift cannot be rejected, because the test value 11.649 is less than the critical value of 12.592.

C.The number of breakdowns is dependent on the shift, because the p-value is .07.

D.The number of breakdowns is independent of the shift, because the test value 12.592 is greater than the critical value of 11.649.

Part 2

Question 3

Correlation is a summary measure that indicates:

A.a curved relationship among the variables

B.the strength of the linear relationship between pairs of variables

C.the magnitude of difference between two variables

D.the rate of change in Y for a one unit change in X

Question 4

In regression analysis, the variable we are trying to explain or predict is called the

A.dependent variable

B.independent variable

C.regression variable

D.residual variable

Question 5

If an estimated regression line has a Y-intercept of –7.5 and a slope of 2.5, then when X = 3, the actual value of Y is:

A.10

B.5

C.unknown

D.0

Part 3

Question 6

Q-Mart is interested in comparing its male and female customers. Q-Mart would like to know if the amount of money spent by its female charge customers differs, on average, from the amount spent by its male charge customers.

To answer this question, an analyst collected random samples of 25 female customers and 22 male customers. Based on these samples, on average, the 25 women charge customers spent $102.23 and the 22 men charge customers spent $86.46. Moreover, the sample standard deviation of the amount charged by the 25 women was $93.393, and the sample standard deviation of the amount charged by the 22 men was $59.695.

Using the procedure advocated by Bluman, at the 10% level of significance, is there sufficient evidence for Q-Mart to conclude that, on average, the amount spent by women charge customers differs from the amount spent by men charge customers.

A.No, the test value does not exceed the critical value.

B.No, the p-value of this test is less than 0.10.

C.Yes, the p-value of this test is greater than 0.10

D.Yes, the test value does not exceed the critical value

Question 7

Multiple myeloma or blood plasma cancer is characterized by increased blood vessel formulation in the bone marrow that is a prognostic factor in survival. One treatment approach used for multiple myeloma is stem cell transplantation with the patient’s own stem cells. The following data represent the bone marrow microvessel density for a sample of 7 patients who had a complete response to a stem cell transplant as measured by blood and urine tests. Two measurements were taken: the first immediately prior to the stem cell transplant, and the second at the time of the complete response.

Patient 1 2 3 4 5 6 7

Before 158 189 202 353 416 426 441

After 284 214 101 227 290 176 290

Suppose you wanted to conduct a test of hypothesis to determine if there is sufficient evidence to conclude that the mean bone marrow microvessel density is higher before the stem cell transplant than after the stem cell transplant? What is the p-value associated with the test of hypothesis you would conduct?

A.p = .114986

B.p = .942597

C.p = .885014

D.p = .057493

Question 8

Results from previous studies showed 79% of all high school seniors from a certain city plan to attend college after graduation. A random sample of 200 high school seniors from this city reveals that 162 plan to attend college. Does this indicate that the percentage has increased from that of previous studies? Test at the 5% level of significance.

Compute the z or t value of the sample test statistic.

A.z = 0.69

B.t = 1.645

C.z = 1.96

D.z = 0.62

Question 9

In an article appearing in Today’s Health a writer states that the average number of calories in a serving of popcorn is 75. To determine if the average number of calories in a serving of popcorn is different from 75, a nutritionist selected a random sample of 20 servings of popcorn and computed the sample mean number of calories per serving to be 78 with a sample standard deviation of 7.

State the null and alternative hypotheses.

A.H0: = 75, H1: 75

B.H0: 75, H1: 75

C.H0: 75, H1: < 75

D.H0: = 75, H1: ≠ 75

Question 10

In an article appearing in Today’s Health a writer states that the average number of calories in a serving of popcorn is 75. To determine if the average number of calories in a serving of popcorn is different from 75, a nutritionist selected a random sample of 20 servings of popcorn and computed the sample mean number of calories per serving to be 78 with a sample standard deviation of 7.

Compute the z or t value of the sample test statistic.

A.t = 1.916

B.t = -1.916

C.z = 1.645

D.z = 1.916

Part 5

Question 11

Confidence intervals are a function of which of the following three things?

A.The sample, the variable of interest, and the degrees of freedom

B.The data in the sample, the confidence level, and the sample size

C.The population, the sample, and the standard deviation

D.The sampling distribution, the confidence level, and the degrees of freedom

Question 12

In order to be accepted into a top university, applicants must score within the top 5% on the SAT exam. Given that SAT test scores are normally distributed with a mean of 1000 and a standard deviation of 200, what is the lowest possible score a student needs to qualify for acceptance into the university?

A.1330

B.1400

C.1250

D.1100

Part 6

Question 13

The continuous distribution characterized by a symmetric, bell-shaped curve is the:

A.binomial distribution

B.Poisson distribution

C.normal distribution

D.exponential distribution

Part 7

Question 14

A pet supplier has a stock of parakeets of which 10% are blue parakeets. A pet store orders 3 parakeets from this supplier. If the supplier selects the parakeets at random, what is the chance that the pet store gets exactly one blue parakeet?

A.0.081

B.0.243

C.0.027

D.0.003

Part 8

Question 15

If 25 tickets are sold and 2 prizes are to be awarded, find the probability that one person will win both prizes if that person buys exactly 2 tickets.

A.1/2300

B.1/300

C.1/700

D.1/600

Part 9

Question 16 3.0 Points

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

Staples, a chain of large office supply stores, sells a line of desktop and laptop computers. Company executives want to know whether the demands for these two types of computers are dependent on one another. Each day's demand for each type of computers is categorized as Low, Medium-Low, Medium-High, or High. The data shown in the table below is based on 200 days of operation. Based on these data, can Staples conclude that demands for these two types of computers are independent? Test at the 5% level of significance.

desktops

low med-low med-high high

low 3 14 14 4 35

laptops med-low 6 18 17 22 63

med-high 13 16 11 16 56

high 8 14 15 9 46

30 62 57 51 200

What is the test value for this hypothesis test?

Answer: Round your answer to two decimal places.

What is the critical value for this hypothesis test?

Answer: Round your answer to two decimal places.

What is the conclusion for this hypothesis test? Choose one.

1. At the .05 level of significance, Staples can conclude that demands for these two types of computers are independent.

2. At the .05 level of significance, Staples can conclude that demands for these two types of computers are dependent.

Answer: Enter only a 1 or 2 for your answer.

Part 10

Question 17

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

The marketing manager of a large supermarket chain would like to determine the effect of shelf space (in feet) on the weekly sales of international food (in hundreds of dollars). A random sample of 12 equal –sized stores is selected, with the following results:

Store Shelf Space(X) Weekly Sales(Y)

1 10 2.0

2 10 2.6

3 10 1.8

4 15 2.3

5 15 2.8

6 15 3.0

7 20 2.7

8 20 3.1

9 20 3.2

10 25 3.0

11 25 3.3

12 25 3.5

Find the equation of the regression line for these data. What is the value of the coefficient of determination? Place your answer, rounded to 3 decimal places, in the blank. Do not use a dollar sign. For example, 0.345 would be a legitimate entry.

Part 11

Question 18

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

Are America's top chief executive officers (CEOs) really worth all that money? One way to answer this question is to look at the annual company percentage increase in revenue versus the CEO's annual percentage salary increase in that same company. Suppose that a random sample of companies yielded the following data:

percent change for corporation 15 12 3 12 28 6 8 2

percent change for CEO 6 17 -4 12 32 -1 7 2

Do these data indicate that the population mean percentage increase in corporate revenue is greater than the population mean percentage increase in CEO salary? Use a 5% level of significance. What is the critical value that you would use to conduct this test of hypothesis? Place your answer, rounded to 3 decimal places, in the blank. For example, 2.345 would be a legitimate entry.

Part 12

Question 19

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

Scores on a mathematics examination appear to follow a normal distribution with mean of 65 and standard deviation of 15. The instructor wishes to give a grade of “C” to students scoring between the 60th and 70th percentiles on the exam.

What score represents the 70th percentile score on the mathematics exam? Place your answer in the blank, rounded to a whole number. For example, 62 would be a legitimate entry.

Part 13

Question 20

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

The manufacturer of a new compact car claims the miles per gallon (mpg) for the gasoline consumption is mound-shaped and symmetric with a mean of 25.9 mpg and a standard deviation of 9.5 mpg. If 30 such cars are tested, what is the probability the average mpg achieved by these 30 cars will be greater than 28?

Answer: Round your answer to 4 decimal places as necessary. For example, 0.1357 would be a legitimate entry.

Part 14

Question 21

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

Find the mean of the probability distribution:

X 0 1 2 3 4

P(X) 0.12 0.16 0.24 0.30 0.18

Round your answer to two decimal place as necessary. For example, 4.56 would be a legitimate entry.

Mean =

Part 15

Question 22

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

The ABC battery company claims that their batteries last at least 100 hours, on average. Your experience with their batteries has been somewhat different, so you decide to conduct a test to see if the company's claim is true. You believe that the mean life is actually less than the 100 hours the company claims. You decide to collect data on the average battery life (in hours) of a random sample of n = 20 batteries. Some of the information related to the hypothesis test is presented below.

Test of H0: 100 versus H1: 100

Sample mean 98.5

Std error of mean 0.777

Assuming the life length of batteries is normally distributed, if you wish to conduct this test using a .05 level of significance, what is the critical value that you should use? Place your answer, rounded to 3 decimal places in the blank. For example, -1.234 would be a legitimate entry.

Part 16

Question 23

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

An ice cream vendor sells three flavors: chocolate, strawberry, and vanilla. Forty five percent of the sales are chocolate, while 30% are strawberry, with the rest vanilla flavored. Sales are by the cone or the cup. The percentages of cones sales for chocolate, strawberry, and vanilla, are 75%, 60%, and 40%, respectively. For a randomly selected sale, define the following events:

= chocolate chosen

= strawberry chosen

= vanilla chosen

= ice cream on a cone

ice cream in a cup

Find the probability that the ice cream was chocolate flavor, given that it was sold in a cup. Place your answer, rounded to 4 decimal places, in the blank. For exampe, 0.3456 would be a legitimate entry.

You'll get a 16.7KB .DOCX file.