Statistics assignment help

Name __________________________

STAT2103

Quiz 4

Multiple Choice

1. The average score of all golfers for a particular course has a mean of 71 and a standard deviation of 3. Suppose 36 golfers played the course today. Find the probability that the average score of the 36 golfers exceeded 72.

a. .1293

b. .0228

c. .3707

d. .4772

2. One year, the distribution of salaries for professional sports players had mean $1.5 million and standard deviation $0.9 million. Suppose a sample of 400 major league players was taken. Find the approximate probability that the average salary of the 400 players that year exceeded $1.1 million.

a. approximately 0

b. approximately 1

c. .2357

d. .7357

3. A Florida newspaper reported on the topics that teenagers most want to discuss with their parents. The findings, the results of a poll, showed that 46% would like more discussion about the family’s financial situation, 37% would like to talk about school, and 30% would like to talk about religion. These and other percentages were based on a national sampling of 532 teenagers. Estimate the proportion of all teenagers who want more family discussions about school. Use a 95% confidence level.

a. .63 ± .041

b. .37 ± .002

c. .63 ± .002

d. .37 ± .041

Short Answer. Write the word or phrase that best completes each statement or answers the question.

4. The amount of time it takes a student to walk from her home to class has a skewed right distribution with a mean of 15 minutes and a standard deviation of 2.4 minutes. If times were collected from 50 randomly selected walks, describe the sampling distribution of

, the sample mean time.

5. A random sample of 50 employees of a large company was asked the question, “Do you participate in the company’s stock purchase plan?” The answers are shown below.

yes no no yes no no yes yes no no no

yes yes yes no yes no no yes yes no yes

yes no yes yes no yes yes yes yes no no

yes yes yes yes yes no yes no yes yes no

yes yes yes yes yes yes

Use a 90% confidence interval to estimate the proportion of employees who participate in the company’s stock purchase plan.

6. A Florida newspaper reports on the topics that teenagers most want to discuss with their parents. The findings, the results of a poll, showed that 46% would like more discussion about the family’s financial situation, 37% would like to talk about school, and 30% would like to talk about religion. These and other percentages were based on a national sampling of 505 teenagers. Estimate the proportion of all teenagers who want more family discussions about religion. Use a 95% confidence level.

7. Let t0 be a particular value of t. Find a value of t0 such that P(t ≤ – t0 or t ≥ t0 ) = 0.10 where df = 14.

8. Suppose you selected a random sample of n = 29 measurements from a normal distribution. Compare the standard normal z value with the corresponding t value for a 95% confidence interval.

9. A random sample of 80 observations produced a mean

= 35.4 and a standard deviation s = 3.1.

a. Find a 90% confidence interval for the population mean μ.

b. Find a 95% confidence interval for μ.

c. Find a 99% confidence interval for μ.

d. What happens to the width of a confidence interval as the value of the confidence coefficient is increased while the sample size is held fixed?

10. The following data represent the scores of a sample of 50 randomly chosen students on a standardized test.

39 48 55 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 91 92 92 93 95 96 97 97 99

a. Identify the target parameter and the point estimator.

b. Write a 95% confidence interval for the mean score of all students who took the test.

c. Test the following hypotheses at the

= 0.05.

H0: µ = 83.5

H1: µ ≠ 83.5

11. How much money does the average professional football fan spend on food at a single football game? That question was posed to 45 randomly selected football fans. The sample results provided a sample mean and standard deviation of $18.00 and $3.15, respectively. Find and interpret a 99% confidence interval for μ.

12. Bonus:

a. Previous research suggests that the average adult drinks 2.5 cups of coffee a day. Jim believes that this number is much higher. Write the null and alternate hypotheses to test his theory. Set up the rejection region for α = .05.

b. To test the above hypotheses, Jim randomly selects 10 people from a normal population.

4 2 1 3 5 3 4 2 3

Using his data, calculate the test statistic. Is there enough statistical evidence to reject the null hypothesis?