.DOCX

# ECO 250 Final Exam

ECO 250 Final

Be sure to round answers to at least two decimals! You will not get credit for the answer 3.1 if the actual answer is 3.1157, but you would get credit for 3.12, 3.116, or 3.1157.

Question 1

The mathematical science that deals with the collection, analysis, and presentation of data is

Economics

Mathematical analysis

Statistics

Data analysis

Question 2

Sampling error is the difference between the __________ and the parameter.

Sample

Sample mode

Statistic

None of the above

Question 3

The __________ is the probability distribution used in place of the normal distribution to calculate a confidence interval when the population standard deviation is unknown.

Uniform distribution

Binomial distribution

Exponential distribution

Student's t-distribution

Question 4

A __________ is a distribution in which the probability of any interval occurring is equal to any other interval with the same width.

Normal distribution

Uniform distribution

Binomial distribution

Student's t-distribution

Question 5

The number of rushing touchdowns for the Minnesota Vikings in a season is an example of

Nominal data

Ratio data

Interval data

Ordinal data

Question 6

Which is a continuous random variable?

The number of students in an ECO 250 class.

The number of births in a hospital on a given day.

The hourly earnings of a call center employee in Boston.

The number of fives obtained in four rolls of a die.

Question 7

The empirical rule states if a distribution is symmetrical and bell-shaped, approximately 68%, 95%, and _______ of its data values will fall within one, two, and three standard deviations above and below the mean, respectively.

99.5%

98%

99.7%

99%

Question 8

__________ is the probability that the interval estimate will include the population parameter of interest, such as a mean.

Significance level

Confidence level

Degrees of freedom

Margin of error

Question 9

The __________ is a variable that represents the probability that any given confidence interval will not contain the true population mean.

Significance level

Degrees of freedom

Confidence level

Margin of error

Question 10

What is an error that occurs when the null hypothesis is rejected when, in reality, it is true?

None of the above

Type I error

Sampling error

Type II error

Question 11

Which is a time series variable?

VISA balances of 30 students on December 31 of this year.

Dollar exchange rates yesterday against 10 other world currencies

Net earnings reported by Xena Corp for the last 10 quarters.

Titles of the top 10 movies in total revenue last week

Question 12

A tire company performs quality-control tests on the monthly output of its best-selling model tire at each of its plants. Each month a random sample of 25 tires is selected from each plant and tested to see if the average tread life of that plant’s tires is above specifications. For one plant, the random sample of 25 tires had a sample mean of 39,500 miles and a sample standard deviation of 3,300 miles. The company performs a hypothesis test at the .05 level of significance to see if there is evidence that the average tread life is greater than 38,000. Based on this sample, the company should:

Reject the null hypothesis and conclude there is evidence that the average tread life is greater than 38,000 miles.

Fail to reject the null hypothesis and conclude there is not evidence that the average tread life is greater than 38,000 miles.

Reject the null hypothesis and conclude there is not evidence that the average tread life is greater than 38,000 miles.

Fail to reject the null hypothesis and conclude there is evidence that the average tread life is greater than 38,000 miles

Question 13

What is the probability of observing a sample mean at least as extreme as the one selected for the hypothesis test, assuming the null hypothesis is true?

p-value

Alpha

Beta

Confidence level

Question 14

Which is not a characteristic of a binomial experiment?

The experiment consists of an infinite number of trials.

Each trial has only two possible outcomes: a success or a failure

Each trial is independent of the other trials in the experiment

The probability of success is equal to one minus the probability of failure

Question 15

A __________ is a continuous distribution that is bell shaped and symmetrical around the mean.

Exponential distribution

Normal distribution

Uniform distribution

Binomial distribution

Question 16 The critical z-score for an 85% confidence level is ________.

1.44

1.28

2.33

1.96

Question 17

YouTube would like to test the hypothesis that the average length of an online video watched by a user is more than 6 minutes. A random sample of 40 people watched online videos that averaged 6.6 minutes in length. The population standard deviation for the length of online videos is 1.7 minutes. YouTube would like to set α=0.05. The p-value for this hypothesis test would be _________.

0.0644

0.0395

0.0129

0.0268

Question 18

A professor would like to test the hypothesis that the average number of minutes that a student needs to complete a statistics exam is equal to 45 minutes. The correct hypothesis statement would be

Question 19

What should you do when the p-value is less than the significance level?

Fail to reject the null hypothesis

Accept the alternative hypothesis

Accept the null hypothesis

Reject the null hypothesis

Question 20

Consider the following set of numbers: 10, 25, 13, 18, 40, 5. Determine the median and variance of these data.

median = 18.5, variance = 12.57

median = 15.5, variance = 157.9

median = 15.5, variance = 35

median = 18.5, variance = 473.83

Question 21

A point estimate, also called a statistic, is a single value that describes the population of interest, with the sample mean being the most common.

True

False

Question 22

The margin of error is the width of the confidence interval between the lower limit and the upper limit.

True

False

Question 23

The alternative hypothesis represents the status quo and involves stating the belief that the population parameter is a specific value and is always associated with the equal sign.

True

False

Question 24

A z-score measures the number of standard deviations a value is from its mode.

True

False

Question 25

Suppose Nike's average stock price this year is $15.00 with a standard deviation of $3.00, and Under Armour's average stock price this year is $24.00 with a standard deviation of $4.00. According to this data, Nike's stock price is more consistent than Under Armour's stock price.

True

False

Question 26

The Central Limit Theorem states that sample means, drawn from a normally distributed population, will be normally distributed.

True

False

Question 27

A low p-value indicates a high probability that the null hypothesis is not true.

True

False

Question 28

If the absolute value of the test statistic is less than the critical value in a two-tailed hypothesis test, then the decision is to reject the null hypothesis.

True

False

Question 29

Consider the hypotheses

H0: Defendant is innocent

H1: Defendant is guilty

If a court acquits every defendant, they will never commit Type II error.

True

False

Question 30

If we do not have evidence to support the alternative hypothesis, then we accept the null hypothesis.

True

False

Question 31

Suppose the average puppy weighs 10 pounds. A sample of 10 puppies yields a sample mean of 13.2 pounds and a sample standard deviation of 2.78 pounds. Assume the population standard deviation is known to be 5.25.You want to test whether the sample mean differs from the population mean of 10 pounds at a 5 percent level of significance using a two-tailed test. What are your null and alternative hypotheses?

Question 32

Suppose the average puppy weighs 10 pounds. A sample of 10 puppies yields a sample mean of 13.2 pounds and a sample standard deviation of 2.78 pounds. Assume the population standard deviation is known to be 5.25.You want to test whether the sample mean differs from the population mean of 10 pounds at a 5 percent level of significance using a two-tailed test. Calculate the test statistic for the sample data.

Question 33

Suppose the average puppy weighs 10 pounds. A sample of 10 puppies yields a sample mean of 13.2 pounds and a sample standard deviation of 2.78 pounds. Assume the population standard deviation is known to be 5.25.You want to test whether the sample mean differs from the population mean of 10 pounds at a 5 percent level of significance using a two-tailed test. State the critical value.

Question 34

Suppose the average puppy weighs 10 pounds. A sample of 10 puppies yields a sample mean of 13.2 pounds and a sample standard deviation of 2.78 pounds. Assume the population standard deviation is known to be 5.25.You want to test whether the sample mean differs from the population mean of 10 pounds at a 5 percent level of significance using a two-tailed test. Determine whether or not the null hypothesis should be rejected.

Fail to reject the null hypothesis.

Reject the null hypothesis.

Question 35

Consider the following data on the number of beers consumed by a sample of football fans during a game:

3 5 0 2 5 3.

Calculate the mean number of beers.

Question 36

Consider the following data on the number of beers consumed by a sample of football fans during a game:

3 5 0 2 5 3.

Calculate the median.

Question 37

Consider the following data on the number of beers consumed by a sample of football fans during a game:

3 5 0 2 5 3.

Calculate the mode (mark all that apply).

0

5

2

3

Question 38

Consider the following data on the number of beers consumed by a sample of football fans during a game:

3 5 0 2 5 3.

Calculate the variance.

Question 39

You check the weather forecast every morning. On average, it is rainy 20 percent of the time. Consider the next 5 days. What is the probability it will be rainy exactly 1 day?

Question 40

You check the weather forecast every morning. On average, it is rainy 20 percent of the time. Consider the next 5 days. What is the probability it will be rainy at most 2 days?

Question 41

The average batter life of the iPhone 4S is reported to be 6.0 hours by Apple. Assume that the population standard deviation for the better life for this cell phone is 30 minutes. A random sample of 50 iPhones had an average better life of 5.7 hours. Determine the margin of error (in hours) for the 90% confidence interval for this sample.

Question 42

The average batter life of the iPhone 4S is reported to be 6.0 hours by Apple. Assume that the population standard deviation for the better life for this cell phone is 30 minutes. A random sample of 50 iPhones had an average better life of 5.7 hours. Determine the lower confidence limit (LCL), in hours, for the 90% confidence interval for this sample.

Question 43

The average batter life of the iPhone 4S is reported to be 6.0 hours by Apple. Assume that the population standard deviation for the better life for this cell phone is 30 minutes. A random sample of 50 iPhones had an average better life of 5.7 hours. Determine the upper confidence limit (UCL), in hours, for the 90% confidence interval for this sample.

Question 44

Consider the following discrete probability distribution.

X P(X)

0 0.2

1 0.3

2 0.4

3 0.1

Total 1.0

Calculate the mean of this distribution.

Question 45

Consider the following discrete probability distribution.

X P(X)

0 0.2

1 0.3

2 0.4

3 0.1

Total 1.0

Calculate the variance of this distribution.

Question 46

The commute time to work for a particular employee follows a continuous uniform distribution with a minimum time of 9 minutes and a maximum time of 25 minutes.

What is the mean of this distribution?

Question 47

The commute time to work for a particular employee follows a continuous uniform distribution with a minimum time of 9 minutes and a maximum time of 25 minutes.

What is the probability that the employee's next commute to work will require less than 10 minutes?

Question 48

The commute time to work for a particular employee follows a continuous uniform distribution with a minimum time of 9 minutes and a maximum time of 25 minutes.

What is the probability that the employee's next commute time will require between 12 minutes and 20 minutes?

Question 49

Consider the following hypothesis:

H1: μ25

Given that calculate the test statistic.

Question 50

Consider the following hypothesis:

H1: μ25

Given that state the critical value.

Question 51

Consider the following hypothesis:

H1: μ25

Given that determine whether or not the null hypothesis should be rejected.

Fail to reject the null hypothesis

Reject the null hypothesis

Question 52

A tire manufacturer selected a random sample of 50 tires of a particular model chosen from the past month’s production and used destructive testing to determine the tread life of each tire. The sample mean was 42,300 miles and the sample standard deviation was 7,500 miles. What is the 95% confidence interval estimate for the tread life of that entire model produced in the past month?

Question 53

Suppose the average number of complaints received by Christiana Hospital from patients is 7.4 every four weeks. Assume the number of complaints per month follows the Poisson distribution.

What is the probability of exactly four complaints during the next four weeks?

Question 54

Suppose the average number of complaints received by Christiana Hospital from patients is 7.4 every four weeks. Assume the number of complaints per month follows the Poisson distribution.

What is the probability of four or more complaints during the next four weeks?

Question 55

Suppose the average number of complaints received by Christiana Hospital from patients is 7.4 every four weeks. Assume the number of complaints per month follows the Poisson distribution.

What is the probability of exactly three complaints during the next two weeks?

Question 56

Zombies eat, on average, 5 brains per day. Assume the actual number of brains eaten per day follows the normal distribution with a standard deviation of 0.29 brains. What is the probability that a zombie will eat exactly 3.2 brains tomorrow?

Be sure to round answers to at least two decimals! You will not get credit for the answer 3.1 if the actual answer is 3.1157, but you would get credit for 3.12, 3.116, or 3.1157.

Question 1

The mathematical science that deals with the collection, analysis, and presentation of data is

Economics

Mathematical analysis

Statistics

Data analysis

Question 2

Sampling error is the difference between the __________ and the parameter.

Sample

Sample mode

Statistic

None of the above

Question 3

The __________ is the probability distribution used in place of the normal distribution to calculate a confidence interval when the population standard deviation is unknown.

Uniform distribution

Binomial distribution

Exponential distribution

Student's t-distribution

Question 4

A __________ is a distribution in which the probability of any interval occurring is equal to any other interval with the same width.

Normal distribution

Uniform distribution

Binomial distribution

Student's t-distribution

Question 5

The number of rushing touchdowns for the Minnesota Vikings in a season is an example of

Nominal data

Ratio data

Interval data

Ordinal data

Question 6

Which is a continuous random variable?

The number of students in an ECO 250 class.

The number of births in a hospital on a given day.

The hourly earnings of a call center employee in Boston.

The number of fives obtained in four rolls of a die.

Question 7

The empirical rule states if a distribution is symmetrical and bell-shaped, approximately 68%, 95%, and _______ of its data values will fall within one, two, and three standard deviations above and below the mean, respectively.

99.5%

98%

99.7%

99%

Question 8

__________ is the probability that the interval estimate will include the population parameter of interest, such as a mean.

Significance level

Confidence level

Degrees of freedom

Margin of error

Question 9

The __________ is a variable that represents the probability that any given confidence interval will not contain the true population mean.

Significance level

Degrees of freedom

Confidence level

Margin of error

Question 10

What is an error that occurs when the null hypothesis is rejected when, in reality, it is true?

None of the above

Type I error

Sampling error

Type II error

Question 11

Which is a time series variable?

VISA balances of 30 students on December 31 of this year.

Dollar exchange rates yesterday against 10 other world currencies

Net earnings reported by Xena Corp for the last 10 quarters.

Titles of the top 10 movies in total revenue last week

Question 12

A tire company performs quality-control tests on the monthly output of its best-selling model tire at each of its plants. Each month a random sample of 25 tires is selected from each plant and tested to see if the average tread life of that plant’s tires is above specifications. For one plant, the random sample of 25 tires had a sample mean of 39,500 miles and a sample standard deviation of 3,300 miles. The company performs a hypothesis test at the .05 level of significance to see if there is evidence that the average tread life is greater than 38,000. Based on this sample, the company should:

Reject the null hypothesis and conclude there is evidence that the average tread life is greater than 38,000 miles.

Fail to reject the null hypothesis and conclude there is not evidence that the average tread life is greater than 38,000 miles.

Reject the null hypothesis and conclude there is not evidence that the average tread life is greater than 38,000 miles.

Fail to reject the null hypothesis and conclude there is evidence that the average tread life is greater than 38,000 miles

Question 13

What is the probability of observing a sample mean at least as extreme as the one selected for the hypothesis test, assuming the null hypothesis is true?

p-value

Alpha

Beta

Confidence level

Question 14

Which is not a characteristic of a binomial experiment?

The experiment consists of an infinite number of trials.

Each trial has only two possible outcomes: a success or a failure

Each trial is independent of the other trials in the experiment

The probability of success is equal to one minus the probability of failure

Question 15

A __________ is a continuous distribution that is bell shaped and symmetrical around the mean.

Exponential distribution

Normal distribution

Uniform distribution

Binomial distribution

Question 16 The critical z-score for an 85% confidence level is ________.

1.44

1.28

2.33

1.96

Question 17

YouTube would like to test the hypothesis that the average length of an online video watched by a user is more than 6 minutes. A random sample of 40 people watched online videos that averaged 6.6 minutes in length. The population standard deviation for the length of online videos is 1.7 minutes. YouTube would like to set α=0.05. The p-value for this hypothesis test would be _________.

0.0644

0.0395

0.0129

0.0268

Question 18

A professor would like to test the hypothesis that the average number of minutes that a student needs to complete a statistics exam is equal to 45 minutes. The correct hypothesis statement would be

Question 19

What should you do when the p-value is less than the significance level?

Fail to reject the null hypothesis

Accept the alternative hypothesis

Accept the null hypothesis

Reject the null hypothesis

Question 20

Consider the following set of numbers: 10, 25, 13, 18, 40, 5. Determine the median and variance of these data.

median = 18.5, variance = 12.57

median = 15.5, variance = 157.9

median = 15.5, variance = 35

median = 18.5, variance = 473.83

Question 21

A point estimate, also called a statistic, is a single value that describes the population of interest, with the sample mean being the most common.

True

False

Question 22

The margin of error is the width of the confidence interval between the lower limit and the upper limit.

True

False

Question 23

The alternative hypothesis represents the status quo and involves stating the belief that the population parameter is a specific value and is always associated with the equal sign.

True

False

Question 24

A z-score measures the number of standard deviations a value is from its mode.

True

False

Question 25

Suppose Nike's average stock price this year is $15.00 with a standard deviation of $3.00, and Under Armour's average stock price this year is $24.00 with a standard deviation of $4.00. According to this data, Nike's stock price is more consistent than Under Armour's stock price.

True

False

Question 26

The Central Limit Theorem states that sample means, drawn from a normally distributed population, will be normally distributed.

True

False

Question 27

A low p-value indicates a high probability that the null hypothesis is not true.

True

False

Question 28

If the absolute value of the test statistic is less than the critical value in a two-tailed hypothesis test, then the decision is to reject the null hypothesis.

True

False

Question 29

Consider the hypotheses

H0: Defendant is innocent

H1: Defendant is guilty

If a court acquits every defendant, they will never commit Type II error.

True

False

Question 30

If we do not have evidence to support the alternative hypothesis, then we accept the null hypothesis.

True

False

Question 31

Suppose the average puppy weighs 10 pounds. A sample of 10 puppies yields a sample mean of 13.2 pounds and a sample standard deviation of 2.78 pounds. Assume the population standard deviation is known to be 5.25.You want to test whether the sample mean differs from the population mean of 10 pounds at a 5 percent level of significance using a two-tailed test. What are your null and alternative hypotheses?

Question 32

Suppose the average puppy weighs 10 pounds. A sample of 10 puppies yields a sample mean of 13.2 pounds and a sample standard deviation of 2.78 pounds. Assume the population standard deviation is known to be 5.25.You want to test whether the sample mean differs from the population mean of 10 pounds at a 5 percent level of significance using a two-tailed test. Calculate the test statistic for the sample data.

Question 33

Suppose the average puppy weighs 10 pounds. A sample of 10 puppies yields a sample mean of 13.2 pounds and a sample standard deviation of 2.78 pounds. Assume the population standard deviation is known to be 5.25.You want to test whether the sample mean differs from the population mean of 10 pounds at a 5 percent level of significance using a two-tailed test. State the critical value.

Question 34

Suppose the average puppy weighs 10 pounds. A sample of 10 puppies yields a sample mean of 13.2 pounds and a sample standard deviation of 2.78 pounds. Assume the population standard deviation is known to be 5.25.You want to test whether the sample mean differs from the population mean of 10 pounds at a 5 percent level of significance using a two-tailed test. Determine whether or not the null hypothesis should be rejected.

Fail to reject the null hypothesis.

Reject the null hypothesis.

Question 35

Consider the following data on the number of beers consumed by a sample of football fans during a game:

3 5 0 2 5 3.

Calculate the mean number of beers.

Question 36

Consider the following data on the number of beers consumed by a sample of football fans during a game:

3 5 0 2 5 3.

Calculate the median.

Question 37

Consider the following data on the number of beers consumed by a sample of football fans during a game:

3 5 0 2 5 3.

Calculate the mode (mark all that apply).

0

5

2

3

Question 38

Consider the following data on the number of beers consumed by a sample of football fans during a game:

3 5 0 2 5 3.

Calculate the variance.

Question 39

You check the weather forecast every morning. On average, it is rainy 20 percent of the time. Consider the next 5 days. What is the probability it will be rainy exactly 1 day?

Question 40

You check the weather forecast every morning. On average, it is rainy 20 percent of the time. Consider the next 5 days. What is the probability it will be rainy at most 2 days?

Question 41

The average batter life of the iPhone 4S is reported to be 6.0 hours by Apple. Assume that the population standard deviation for the better life for this cell phone is 30 minutes. A random sample of 50 iPhones had an average better life of 5.7 hours. Determine the margin of error (in hours) for the 90% confidence interval for this sample.

Question 42

The average batter life of the iPhone 4S is reported to be 6.0 hours by Apple. Assume that the population standard deviation for the better life for this cell phone is 30 minutes. A random sample of 50 iPhones had an average better life of 5.7 hours. Determine the lower confidence limit (LCL), in hours, for the 90% confidence interval for this sample.

Question 43

The average batter life of the iPhone 4S is reported to be 6.0 hours by Apple. Assume that the population standard deviation for the better life for this cell phone is 30 minutes. A random sample of 50 iPhones had an average better life of 5.7 hours. Determine the upper confidence limit (UCL), in hours, for the 90% confidence interval for this sample.

Question 44

Consider the following discrete probability distribution.

X P(X)

0 0.2

1 0.3

2 0.4

3 0.1

Total 1.0

Calculate the mean of this distribution.

Question 45

Consider the following discrete probability distribution.

X P(X)

0 0.2

1 0.3

2 0.4

3 0.1

Total 1.0

Calculate the variance of this distribution.

Question 46

The commute time to work for a particular employee follows a continuous uniform distribution with a minimum time of 9 minutes and a maximum time of 25 minutes.

What is the mean of this distribution?

Question 47

The commute time to work for a particular employee follows a continuous uniform distribution with a minimum time of 9 minutes and a maximum time of 25 minutes.

What is the probability that the employee's next commute to work will require less than 10 minutes?

Question 48

The commute time to work for a particular employee follows a continuous uniform distribution with a minimum time of 9 minutes and a maximum time of 25 minutes.

What is the probability that the employee's next commute time will require between 12 minutes and 20 minutes?

Question 49

Consider the following hypothesis:

H1: μ25

Given that calculate the test statistic.

Question 50

Consider the following hypothesis:

H1: μ25

Given that state the critical value.

Question 51

Consider the following hypothesis:

H1: μ25

Given that determine whether or not the null hypothesis should be rejected.

Fail to reject the null hypothesis

Reject the null hypothesis

Question 52

A tire manufacturer selected a random sample of 50 tires of a particular model chosen from the past month’s production and used destructive testing to determine the tread life of each tire. The sample mean was 42,300 miles and the sample standard deviation was 7,500 miles. What is the 95% confidence interval estimate for the tread life of that entire model produced in the past month?

Question 53

Suppose the average number of complaints received by Christiana Hospital from patients is 7.4 every four weeks. Assume the number of complaints per month follows the Poisson distribution.

What is the probability of exactly four complaints during the next four weeks?

Question 54

Suppose the average number of complaints received by Christiana Hospital from patients is 7.4 every four weeks. Assume the number of complaints per month follows the Poisson distribution.

What is the probability of four or more complaints during the next four weeks?

Question 55

Suppose the average number of complaints received by Christiana Hospital from patients is 7.4 every four weeks. Assume the number of complaints per month follows the Poisson distribution.

What is the probability of exactly three complaints during the next two weeks?

Question 56

Zombies eat, on average, 5 brains per day. Assume the actual number of brains eaten per day follows the normal distribution with a standard deviation of 0.29 brains. What is the probability that a zombie will eat exactly 3.2 brains tomorrow?

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