In the following multiple choice questions, please circle the correct answer.

1. Which of the following statements is false?

a. The t distribution is symmetric about zero

b. The t distribution is more spread out than the standard normal distribution

c. As the degrees of freedom get smaller, the t-distribution’s dispersion gets smaller

d. The t distribution is mound-shaped

2. For statistical inference about the mean of a single population when the population standard deviation is unknown, the degrees for freedom for the t distribution equal n-1 because we lose one degree of freedom by using the:

a. sample mean as an estimate of the population mean

b. sample standard deviation as an estimate of the population standard deviation

c. sample proportion as an estimate of the population proportion

d. sample size as an estimate of the population size

3. In testing the hypotheses

<<<EQUATION>>>Null hypothesis: mu = 200

<<<EQUATION>>>Alternative hypothesis: mu less than 200

the sample mean is found to be 120. The null hypothesis:

a. should be rejected

b. should not be rejected

c. should be rejected only if n > 30

d. none of the above answers is correct

4. For a sample of size 20 taken from a normally distributed population with standard deviation equal to 5, a 90% confidence interval for the population mean would require the use of:

a. t = 1.328

b. t = 1.729

c. t = 2.12

d. z = 1.645

5. Under which of the following circumstances is it impossible to construct a confidence interval for the population mean?

a. A non-normal population with a large sample and an unknown population variance

b. A normal population with a large sample and a known population variance

c. Non-normal population with a small sample and an unknown population variance

d. A normal population with a small sample and an unknown population variance

6. Suppose that a one-tail t test is being applied to find out if the population mean is less than 100. The level of significance is .05 and 25 observations were sampled. The rejection region is:

a. t > 1.708

b. t < -1. 711

c. t > 1.318

d. t < -1.316

7. Which of the following is true about the t distribution?

a. Approaches the normal distribution as its degrees of freedom increase

b. Assumes the population is normally distributed

c. It is more spread out than the standard normal distribution

d. All of the above statements are true

8. A random sample of size 20 taken from a normally distributed population resulted in a sample variance of 32. The lower limit of a 90% confidence interval for the population variance would be:

a. 52.185

b. 20.375

c. 20.170

d. 54.931

9. A random sample of size 15 taken from a normally distributed population revealed a sample mean of 75 and a sample variance of 25. The upper limit of a 95% confidence interval for the population mean would equal:

a. 77.769

b. 72.231

c. 72.727

d. 77.273

10. Based on sample data, the 90% confidence interval limits for the population mean are

LCL = 170.86 UCL = 195.42.

If the 10% level of significance were used in testing the hypotheses

<<<EQUATION>>>Null: mu = 201

<<<EQUATION>>>Alt: mu not equal to 201,

the null hypothesis:

a. would be rejected

b. would not be rejected

c. would have to be revised

d. None of the above

Problem

11. A random sample of 10 university students was surveyed to determine the amount of time spent weekly using a personal computer. The times are:

<<<EQUATION>>>

If the times are normally distributed with a standard deviation of 5.2 hours, estimate with 90% confidence the mean weekly time spent using a personal computer by all university students.

12. How large a sample of state employees should be taken if we want to estimate with 98% confidence the mean salary to within $2,000. The population standard deviation is assumed to be $10,500.

13. A financial analyst wanted to determine the mean annual return on mutual funds. A random sample of 60 returns shows a mean of 12%. If the population standard deviation is assumed to be 4%, estimate with 95% confidence the mean annual return on all mutual funds.

14. A survey of 100 retailers revealed that the mean after-tax profit was $80,000. If we assume that the population standard deviation is $15,000, determine the 95% confidence interval estimate of the mean after-tax profit for all retailers.

15. A normal population has a standard deviation of 15. How large a sample should be drawn to estimate with 95% confidence the population mean to within 1.5?

Problem

16. A random sample of 10 observations was drawn from a normally distributed population. These are:

<<<EQUATION>>>

Test to determine if we can infer at the 5% significance level that the population mean is less than 6.

Answer Key

1.

> c

2.

> a

3.

> d

4.

> d

5.

> c

6.

> b

7.

> d

8.

> c

9.

> a

10.

> a

11.

> 6.5952 to 12.0048

12.

> 150

13.

> 10.988% to 13.012%

14.

> $77,060 to $ 82,940

15.

> 385

16.

> <<<EQUATION>>>

<<<EQUATION>>>

Rejection region: t < -t = ?

Test statistic: t = -3.0

Conclusion: Reject <<<EQUATION>>>. Yes.