# Maths – week 3 homework

1) Many firms use on-the-job training to teach their employees computer programming. Suppose you work in the personnel department of a firm that just finished training a group of its employees to program, and you have been requested to review the performance of one of the trainees on the final test that was given to all trainees. The mean and standard deviation of the test scores are 79 and 2, respectively, and the distribution of scores is mound-shaped and symmetric. Suppose the trainee in question received a score of 76. Compute the trainee’s z-score. 1) ________

Z= ( 76-79)/2= -1.5

A) z = 0.94 B) z = -1.50 C) z = -3 D) z = -6

2) The amount spent on textbooks for the fall term was recorded for a sample of five hundred university students. The mean expenditure was calculated to be $500 and the standard deviation of the expenditures was calculated to be $100. Suppose a randomly selected student reported that their textbook expenditure was $700. Calculate the z-score for this student’s textbook expenditure. 2) ________

Z= ( 700-500) / 100= 2

A) +2 B) +3 C) -3 D) -2

3) A radio station claims that the amount of advertising each hour has a mean of 15 minutes and a standard deviation of 1.5 minutes. You listen to the radio station for 1 hour and observe that the amount of advertising time is 9 minutes. Calculate the z-score for this amount of advertising time. 3) ________

Z= ( 9-15)/1.5= -4

A) z = -4.00 B) z = 0.50 C) z = 4.00 D) z = -9

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

4) A study was designed to investigate the effects of two variables (1) a student’s level of mathematical anxiety and (2) teaching method on a student’s achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 310 and a standard deviation of 50 on a standardized test. Find and interpret the z-score of a student who scored 490 on the standardized test.

4) _______________

5) The following data represent the scores of 50 students on a statistics exam. The mean score is 80.02, and the standard deviation is 11.9.

39 51 59 63 66 68 68 69 70 71

71 71 73 74 76 76 76 77 78 79

79 79 79 80 80 82 83 83 83 85

85 86 86 88 88 88 88 89 89 89

90 90 91 91 92 95 96 97 97 98

Find the z-scores for the highest and lowest exam scores. 5) _______________

1) Suppose you selected a random sample of n = 7 measurements from a normal distribution. Compare the standard normal z value with the corresponding t value for a 90% confidence interval. 1)

_______________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

2) An educator wanted to look at the study habits of university students. As part of the research, data was collected for three variables – the amount of time (in hours per week) spent studying, the amount of time (in hours per week) spent playing video games and the GPA – for a sample of 20 male university students. As part of the research, a 95% confidence interval for the average GPA of all male university students was calculated to be: (2.95, 3.10). Which of the following statements is true? 2) ________

A) In construction of the confidence interval, a z-value was used.

B) In construction of the confidence interval, a t-value with 19 degrees of freedom was used.

C) In construction of the confidence interval, a t-value with 20 degrees of freedom was used.

D) In construction of the confidence interval, a z-value with 20 degrees of freedom was used.

3) You are interested in purchasing a new car. One of the many points you wish to consider is the resale value of the car after 5 years. Since you are particularly interested in a certain foreign sedan, you decide to estimate the resale value of this car with a 95% confidence interval. You manage to obtain data on 17 recently resold 5-year-old foreign sedans of the same model. These 17 cars were resold at an average price of $12,610 with a standard deviation of $700. What is the 95% confidence interval for the true mean resale value of a 5- year-old car of this model? 3) ________

A) 12,610 ± 2.120(700/sqrt(16)) B) 12,610 ± 2.120(700/sqrt(17))

C) 12,610 ± 2.110(700/sqrt(17)) D) 12,610 ± 1.960(700/sqrt(17))

4) A revenue department is under orders to reduce the time small business owners spend filling out pension form ABC-5500. Previously the average time spent on the form was 5.7 hours. In order to test whether the time to fill out the form has been reduced, a sample of 86 small business owners who annually complete the form was randomly chosen, and their completion times recorded. The mean completion time for ABC-5500 form was 5.5 hours with a standard deviation of 2.3 hours. In order to test that the time to complete the form has been reduced, state the appropriate null and alternative hypotheses. 4) ________

A) H with subscript((0)): μ = 5.7

H with subscript((a)): μ > 5.7 B) H with subscript((0)): μ = 5.7

H with subscript((a)): μ ≠ 5.7 C) H with subscript((0)): μ > 5.7

H with subscript((a)): μ < 5.7 D) H with subscript((0)): μ = 5.7

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

1) Which statement best describes a parameter? 1) ________

A) A parameter is an unbiased estimate of a statistic found by experimentation or polling.

B) A parameter is a numerical measure of a population that is almost always unknown and must be estimated.

C) A parameter is a level of confidence associated with an interval about a sample mean or proportion.

D) A parameter is a sample size that guarantees the error in estimation is within acceptable limits.

2) A study was conducted to determine what proportion of all college students considered themselves as full-time students. A random sample of 300 college students was selected and 210 of the students responded that they considered themselves full-time students. Which of the following would represent the target parameter of interest? 2) ________

A) μ B) p

3) A revenue department is under orders to reduce the time small business owners spend filling out pension form ABC-5500. Previously the average time spent on the form was 5.7 hours. In order to test whether the time to fill out the form has been reduced, a sample of 86 small business owners who annually complete the form was randomly chosen, and their completion times recorded. The mean completion time for ABC-5500 form was 5.5 hours with a standard deviation of 2.3 hours. In order to test that the time to complete the form has been reduced, state the appropriate null and alternative hypotheses. 3) ________

A) H with subscript((0)): μ = 5.7

H with subscript((a)): μ > 5.7 B) H with subscript((0)): μ > 5.7

H with subscript((a)): μ < 5.7 C) H with subscript((0)): μ = 5.7

H with subscript((a)): μ < 5.7 D) H with subscript((0)): μ = 5.7

H with subscript((a)): μ ≠ 5.7

4) A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has determined that home delivery will be successful only if the average time spent on a delivery does not exceed 37 minutes. The owner has randomly selected 15 customers and delivered pizzas to their homes. What hypotheses should the owner test to demonstrate that the pizza delivery will not be successful? 4) ________

A) H with subscript((0)): μ = 37 vs. H with subscript((a)): μ ≠ 37 B) H with subscript((0)): μ = 37 vs. H with subscript((a)): μ > 37

C) H with subscript((0)): μ < 37 vs. H with subscript((a)): μ = 37 D) H with subscript((0)): μ = 37 vs. H with subscript((a)): μ < 3

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