# In a math class - Expert Answers

In a math class with 30 students enrolled, 23 students are female and 7 students are male. Suppose a random sample of 5 students is taken. What is the probability that exactly 1 of the 5 selected is a male?

At a particular car dealership, it has been calculated over time that customers who test drive a vehicle have a 7% chance of purchasing a car on the same day. Suppose that a salesman, in one day, takes four customers on a test drive of one of the vehicles at the dealership.

a.)What is the probability that none of the customers purchase a vehicle that day?

b.)What is the probability that at least one of the customers purchase a vehicle that day?

c.)What is the expected number of vehicles sold for every four customers that take a test drive?

A zip-code is a five-digit number identifying where in the U.S. an address is located. The first four digits in a zip-code can be any number 0-9, but the fifth digit cannot be 0. In addition to this, each address has a “plus-four” code that more specifically identifies the location of an address within a town or city. Similar to the main five-digit zip-code, the first three digits in the “plus-four” code can be 0-9, but the fourth digit cannot be 0.

a.) How many five-digit zip codes are possible in the U.S.?

b.)How many “plus-four” zip codes are possible in the U.S. (remember, a “plus-four” zip code is the five-digit zip-code plus the additional four)?

Question 1

Assume that you are using a significance level of á = 0.05 to test the claim that p1 = p2. Use the given sample sizes and the number of hits to find the z test statistic for hypothesis testing. A report on the nightly news program said that 10 108 households with dogs were stolen and 20 208 without dogs were stolen.

A) z = -0041

B) z = -0.102

C) z = 0.000

D) z = -0173

2. Build confidence interval indicated by the difference between the two population means. Suppose that the two samples are independent simple random samples selected from populations with normal distribution. Do not assume that the population standard deviations are equal. A researcher was interested in comparing the resting pulse rate of people who exercise regularly and pulse rates of people who do not exercise regularly. She obtained independent simple random samples of 16 people who do not exercise regularly and 12 people who exercise regularly. Pulse rates at rest (beats per minute) were recorded and summary statistics are as follows.

"DO NOT EXERCISE

REGULARLY

_X1 = 72.3 BEATS / MIN

S1 = 10.9 BEATS / MIN

N1 = 16

Exercise regularly

_X2 = 68.1 BEATS / MIN

S2 = 8.2 BEATS / MIN

N2 = 12

Construct a confidence interval of 95% for ì1 - ì2, the difference between the average pulse frequency of people who do not exercise regularly and pulse frequency of average people who exercise regularly.

-3.22 Beats / min <ì1 - ì2 <11.62 beats / min

-3.55 Beats / min <ì1 - ì2 <11.95 beats / min

-3.74 Beats / min <ì1 - ì2 <12.14 beats / min

-4.12 Beats / min <ì1 - ì2 <14.72 beats / min

Suppose the data are normally distributed and the number of observations is greater than fifty. Find the critical value z used to test the null hypothesis. á = 0.05 for a two-tailed test.

A) ± 1.96

B) -1.96

C) ± 1.64

D) 1.96

A) ± 1.96

Use the given data to find the equation of the regression line. Rounding the final values to three significant digits, if necessary.

X 1 3 5 7 9

Y 143 116 100 98 90

A) Y = -150.7 + 6.8x

B) Y = 150.7 - 6.8x

C) Y = 140.4 - 6.2x

D) Y = -140.4 + 6.2x

Use a computer program to find the multiple regression equation. Can the equation be used for prediction? An anti-snuff group used the data in the table to link carbon monoxide various brands of cigarettes and their content

ART CO NIC

15 1.2 16

15 1.2 16

17 1.0 16

6 0.8 9

1 0.1 1

8 0.8 8

10 0.8 10

17 1.0 16

15 1.2 15

11 0.7 9

18 1.4 18

16 1.0 15

10 0.8 9

7 0.5 5

18 1.1 16

CO = carbon monoxide

TAR = tar

NIC = nicotine

a) CO = 1.37 - 5.53TAR + 133NIC; Yes, because the R2 is high

b) CO = 1.37 + 5.50TAR - 138NIC; Yes, because the p value is high

c) CO = 1.3 + 5.5TAR - 1.3NIC; Yes, because the R2 is low

d) CO = 1.25 + 1.55TAR - 5.79NIC; Yes because the p is low

Find the unexplained variation to the data below. Paired data show test scores and hours of preparation for 5 students randomly selected. The equation of the regression line is = 44.8447 + 3.52427 x. Find the variation does not explcada. x hours of preparation | 2 May 9 June 10 ____________________ | _______________________ | and test scores | 64 48 72 73 80

A) 511 724

B) 87.4757

C) 599.2

D) 96 103

Use the information given to calculate the coefficient of determination. A regression equation is obtained for a set of paired data. It was found that the total variation is 24.488, explained variation is 15,405, and the unexplained variation is 9,083. Calculate the coefficient of determination

A) 0629

B) 0590

C) 1590

D) 0.371

9. Dados the linear correlation coefficient r and the sample size n, determine the críiticos r values and use them to establish whether the given r represents a significant or linear correlation. Use a significance level of 0.05. r = 0.75, n = 9

A) Critical values: r = ± 0.666, there is a significant linear correlation

B) Critical values: r = 0.666, there is a significant linear correlation

C) Critical values: r = - 0.666, there is a significant linear correlation

D) Critical values: r = ± 0.666, significant correlation Linal

Use the given data to find the best predicted value of the response variable. Six pairs of data gives r = 0.789 and the regression equation What is the best predicted for x = 5 value?

A) 22.0

B) 18.0

C) 18.5

D) 19.0

Find standard error of the estimate for the data below. Paired data show test scores and hours of preparation for 5 students randomly selected. The equation of the regression line is Y = 44.8447 + 3.52427 x. Find standard error of the estimate. x hours of preparation X 5 2 9 6 10 ____________________ | _______________________ | Y 64 48 72 73 80

A) 4.1097

B) 7.1720

C) 5.3999

D) 13 060

A) 58 < y < 82

B) 62 < y < 78

C) 35 < y < 104

D) 32 < y < 104

Find the total variation for the data below. Paired data show test scores and hours of preparation for 5 students randomly selected. The equation of the regression line is Y = 44.8447 + 3.52427 x. Find the total variation. x hours of preparation

X 5 2 9 6 10_________________ | _______________________ | and test scores Y 64 48 72 73 80

A) 599.2

B) 498 103

C) 511,724

D) 87.4757

Find the variance explained for the following data. Paired data show test scores and hours of preparation for 5 students randomly selected. The equation of the regression line is = 44.8447 + 3.52427 x. Find the explcada variation. x hours of preparation X 5 2 9 6 10____________________ | _______________________ | and test scores Y 64 48 72 73 80

A) 498 103

B) 511 724

C) 87.4757

D) 599.2

Use a computer program to obtain multiple regression equation. Use the estimated equation to find the predicted value. A health specialist collected the data in the table to see if the pulses can be explained by exercise and smoking. For exercise, he assigned 1 to if and 2 to no. For smoking, if assigned 1 to 2 to no. Then use the results to predict the pulse rate of a person whose value was 1 year and whose value was smoking PULSO EXERCISE 1. SMOKING

97 2 2

88 1 2

69 1 2

67 1 2

83 1 2

77 1 2

66 2 2

78 2 2

73 1 1

67 1 1

55 1 2

82 1 1

70 1 2

55 1 2

76 1 2

A) 70 beats / min

B) 74 beats / min

C) 81 beats / min

D) 77 beats / min

Use a computer program to find the multiple regression equation, R2, R2 and p-value adjusted. An anti-snuff group used the data in the table to link carbon monoxide various brands of cigarettes and content of tar and nicotine. Note: CO = carbon monoxide TAR = tar NIC = nicotine

CO TAR NIC

15 1.2 16

15 1.2 16

17 1.0 16

6 0.8 9

1 0.1 1

8 0.8 8

10 0.8 10

17 0.1 16

15 1.2 15

11 0.7 9

18 1.4 18

16 1.0 1.5

10 0.8 9

7 0.5 5

18 1.1 16

A) 0976, 0921, 0002

B) 0.943, 0.934, 0.000

C) 0.931, 0.902, 0.000

D) 0861, 0900, 0015

Use the results shown to answer the question. A collection of data pairs is the number of years students have studied Spanish and their scores on a test of Spanish language skills. a computer program was used to obtain the linear least squares regression, and computer output shown below. Along with the data of paired samples, the program also gave a value x 2 (years of study) to be used to predict the test score.

The regression equation is

Score = 31.55 + 10.9 years

Predictor Coef. T P

Constant 31.55 6.36 4.96 0,000

10.90 1,744 6.25 0,000 years

S = 5,651 R2 R2 = 83.0% (Adjusted) = 82.7%

predicted values

Est IP 95% 95%

3,168 53.35 (42.72, 63.98) (31.61,75.09)

SD: standard deviation

What percent of the total variation in test scores can be explained by the linear relationship between the years of study and test scores?

A) 82.7%

B) 17.0%

C) 91.1%

D) 83.0%

At a particular car dealership, it has been calculated over time that customers who test drive a vehicle have a 7% chance of purchasing a car on the same day. Suppose that a salesman, in one day, takes four customers on a test drive of one of the vehicles at the dealership.

a.)What is the probability that none of the customers purchase a vehicle that day?

b.)What is the probability that at least one of the customers purchase a vehicle that day?

c.)What is the expected number of vehicles sold for every four customers that take a test drive?

A zip-code is a five-digit number identifying where in the U.S. an address is located. The first four digits in a zip-code can be any number 0-9, but the fifth digit cannot be 0. In addition to this, each address has a “plus-four” code that more specifically identifies the location of an address within a town or city. Similar to the main five-digit zip-code, the first three digits in the “plus-four” code can be 0-9, but the fourth digit cannot be 0.

a.) How many five-digit zip codes are possible in the U.S.?

b.)How many “plus-four” zip codes are possible in the U.S. (remember, a “plus-four” zip code is the five-digit zip-code plus the additional four)?

Question 1

Assume that you are using a significance level of á = 0.05 to test the claim that p1 = p2. Use the given sample sizes and the number of hits to find the z test statistic for hypothesis testing. A report on the nightly news program said that 10 108 households with dogs were stolen and 20 208 without dogs were stolen.

A) z = -0041

B) z = -0.102

C) z = 0.000

D) z = -0173

2. Build confidence interval indicated by the difference between the two population means. Suppose that the two samples are independent simple random samples selected from populations with normal distribution. Do not assume that the population standard deviations are equal. A researcher was interested in comparing the resting pulse rate of people who exercise regularly and pulse rates of people who do not exercise regularly. She obtained independent simple random samples of 16 people who do not exercise regularly and 12 people who exercise regularly. Pulse rates at rest (beats per minute) were recorded and summary statistics are as follows.

"DO NOT EXERCISE

REGULARLY

_X1 = 72.3 BEATS / MIN

S1 = 10.9 BEATS / MIN

N1 = 16

Exercise regularly

_X2 = 68.1 BEATS / MIN

S2 = 8.2 BEATS / MIN

N2 = 12

Construct a confidence interval of 95% for ì1 - ì2, the difference between the average pulse frequency of people who do not exercise regularly and pulse frequency of average people who exercise regularly.

-3.22 Beats / min <ì1 - ì2 <11.62 beats / min

-3.55 Beats / min <ì1 - ì2 <11.95 beats / min

-3.74 Beats / min <ì1 - ì2 <12.14 beats / min

-4.12 Beats / min <ì1 - ì2 <14.72 beats / min

Suppose the data are normally distributed and the number of observations is greater than fifty. Find the critical value z used to test the null hypothesis. á = 0.05 for a two-tailed test.

A) ± 1.96

B) -1.96

C) ± 1.64

D) 1.96

A) ± 1.96

Use the given data to find the equation of the regression line. Rounding the final values to three significant digits, if necessary.

X 1 3 5 7 9

Y 143 116 100 98 90

A) Y = -150.7 + 6.8x

B) Y = 150.7 - 6.8x

C) Y = 140.4 - 6.2x

D) Y = -140.4 + 6.2x

Use a computer program to find the multiple regression equation. Can the equation be used for prediction? An anti-snuff group used the data in the table to link carbon monoxide various brands of cigarettes and their content

ART CO NIC

15 1.2 16

15 1.2 16

17 1.0 16

6 0.8 9

1 0.1 1

8 0.8 8

10 0.8 10

17 1.0 16

15 1.2 15

11 0.7 9

18 1.4 18

16 1.0 15

10 0.8 9

7 0.5 5

18 1.1 16

CO = carbon monoxide

TAR = tar

NIC = nicotine

a) CO = 1.37 - 5.53TAR + 133NIC; Yes, because the R2 is high

b) CO = 1.37 + 5.50TAR - 138NIC; Yes, because the p value is high

c) CO = 1.3 + 5.5TAR - 1.3NIC; Yes, because the R2 is low

d) CO = 1.25 + 1.55TAR - 5.79NIC; Yes because the p is low

Find the unexplained variation to the data below. Paired data show test scores and hours of preparation for 5 students randomly selected. The equation of the regression line is = 44.8447 + 3.52427 x. Find the variation does not explcada. x hours of preparation | 2 May 9 June 10 ____________________ | _______________________ | and test scores | 64 48 72 73 80

A) 511 724

B) 87.4757

C) 599.2

D) 96 103

Use the information given to calculate the coefficient of determination. A regression equation is obtained for a set of paired data. It was found that the total variation is 24.488, explained variation is 15,405, and the unexplained variation is 9,083. Calculate the coefficient of determination

A) 0629

B) 0590

C) 1590

D) 0.371

9. Dados the linear correlation coefficient r and the sample size n, determine the críiticos r values and use them to establish whether the given r represents a significant or linear correlation. Use a significance level of 0.05. r = 0.75, n = 9

A) Critical values: r = ± 0.666, there is a significant linear correlation

B) Critical values: r = 0.666, there is a significant linear correlation

C) Critical values: r = - 0.666, there is a significant linear correlation

D) Critical values: r = ± 0.666, significant correlation Linal

Use the given data to find the best predicted value of the response variable. Six pairs of data gives r = 0.789 and the regression equation What is the best predicted for x = 5 value?

A) 22.0

B) 18.0

C) 18.5

D) 19.0

Find standard error of the estimate for the data below. Paired data show test scores and hours of preparation for 5 students randomly selected. The equation of the regression line is Y = 44.8447 + 3.52427 x. Find standard error of the estimate. x hours of preparation X 5 2 9 6 10 ____________________ | _______________________ | Y 64 48 72 73 80

A) 4.1097

B) 7.1720

C) 5.3999

D) 13 060

A) 58 < y < 82

B) 62 < y < 78

C) 35 < y < 104

D) 32 < y < 104

Find the total variation for the data below. Paired data show test scores and hours of preparation for 5 students randomly selected. The equation of the regression line is Y = 44.8447 + 3.52427 x. Find the total variation. x hours of preparation

X 5 2 9 6 10_________________ | _______________________ | and test scores Y 64 48 72 73 80

A) 599.2

B) 498 103

C) 511,724

D) 87.4757

Find the variance explained for the following data. Paired data show test scores and hours of preparation for 5 students randomly selected. The equation of the regression line is = 44.8447 + 3.52427 x. Find the explcada variation. x hours of preparation X 5 2 9 6 10____________________ | _______________________ | and test scores Y 64 48 72 73 80

A) 498 103

B) 511 724

C) 87.4757

D) 599.2

Use a computer program to obtain multiple regression equation. Use the estimated equation to find the predicted value. A health specialist collected the data in the table to see if the pulses can be explained by exercise and smoking. For exercise, he assigned 1 to if and 2 to no. For smoking, if assigned 1 to 2 to no. Then use the results to predict the pulse rate of a person whose value was 1 year and whose value was smoking PULSO EXERCISE 1. SMOKING

97 2 2

88 1 2

69 1 2

67 1 2

83 1 2

77 1 2

66 2 2

78 2 2

73 1 1

67 1 1

55 1 2

82 1 1

70 1 2

55 1 2

76 1 2

A) 70 beats / min

B) 74 beats / min

C) 81 beats / min

D) 77 beats / min

Use a computer program to find the multiple regression equation, R2, R2 and p-value adjusted. An anti-snuff group used the data in the table to link carbon monoxide various brands of cigarettes and content of tar and nicotine. Note: CO = carbon monoxide TAR = tar NIC = nicotine

CO TAR NIC

15 1.2 16

15 1.2 16

17 1.0 16

6 0.8 9

1 0.1 1

8 0.8 8

10 0.8 10

17 0.1 16

15 1.2 15

11 0.7 9

18 1.4 18

16 1.0 1.5

10 0.8 9

7 0.5 5

18 1.1 16

A) 0976, 0921, 0002

B) 0.943, 0.934, 0.000

C) 0.931, 0.902, 0.000

D) 0861, 0900, 0015

Use the results shown to answer the question. A collection of data pairs is the number of years students have studied Spanish and their scores on a test of Spanish language skills. a computer program was used to obtain the linear least squares regression, and computer output shown below. Along with the data of paired samples, the program also gave a value x 2 (years of study) to be used to predict the test score.

The regression equation is

Score = 31.55 + 10.9 years

Predictor Coef. T P

Constant 31.55 6.36 4.96 0,000

10.90 1,744 6.25 0,000 years

S = 5,651 R2 R2 = 83.0% (Adjusted) = 82.7%

predicted values

Est IP 95% 95%

3,168 53.35 (42.72, 63.98) (31.61,75.09)

SD: standard deviation

What percent of the total variation in test scores can be explained by the linear relationship between the years of study and test scores?

A) 82.7%

B) 17.0%

C) 91.1%

D) 83.0%

You'll get 1 file (18.3KB)