Statistics Name:__________________________________

Chapters 6 and 7 PRACTICE TEST

If you need additional space, use an extra sheet. If you used a calc for any prob/stats, write what you typed in. 1. Construct the confidence interval for 𝜇 given the following:

a) c = 0.9, �̅� = 15 𝜎 = 3, and n = 80.

b) c = 0.95, �̅� = 15 𝜎 = 3, and n = 50.

c) Give two reasons why the confidence interval in part (b) is

wider.

2. The formula for the margin of error E for a confidence

interval (given a population standard deviation) is shown

below. Solve it for n, the minimum sample size.

𝐸 = 𝑧𝑐

𝜎

√𝑛

3. A soccer ball manufacturer wants to estimate the mean

circumference of soccer balls within 0.1 inch.

a) Determine the minimum sample size required to construct a

95% confidence interval for the population mean, assuming the

population standard deviation is 0.25 inch.

b) Repeat part (a) using a pop. standard deviation of 0.3 inch.

c) Why does part (b) have a larger required sample size?

4. In constructing a 95% confidence interval for the mean

travel time it takes workers, one arrives at (18.3, 23.7).

State whether each interpretation below is true or false.

a) “95% of the 45 workers take between 18.3 and 23.7 minutes

to get to work”

b) “There is a 95% chance that the mean time it takes all

workers to get to work is between 18.3 and 23.7 minutes.”

c) “We are 95% confident that the mean time it takes all

workers to get to work is between 18.3 and 23.7 minutes.”

5. According to the international basketball rules, a ball is

properly inflated if when dropped from shoulder height it

rebounds to 1.3 meters. A sample of 25 balls is randomly

tested and found to have a mean rebound height of 1.4 m

with a sample standard deviation of 0.2 m.

a) Construct a 95% confidence interval for the population mean.

b) Based on your answer to part (a), does it appear these balls

are properly inflated according to the rules?

6. Find point estimates (�̂� 𝑎𝑛𝑑 �̂�) of p and q in the situation

where in a survey of 455 employees, 208 support retirement

plan A offered by the company.

�̂� =____________ �̂� = ____________

Verify why we would be justified in approximating the

sampling distribution for �̂� with a normal distribution.

Condition 1:

Condition 2:

7. For the situation in Problem 6, construct a 99% confidence

interval for the population proportion.

Interpret the confidence interval you constructed above.

With 99% confidence, you can say that the population

proportion of employees who support retirement plan A is

between 39.7% and 51.7%.

8. a) What is the definition of type I error?

Type I error occurs when one incorrectly rejects a null

hypothesis when it was in fact true. The p-value of a hypothesis

test indicates the probability of type I error occurring.

b) If the level of significance is set to be 𝛼 = 0.05, what is the

probability of committing type I error? 5%. The significance

level sets the acceptable probability of committing type I error.

9. The statements below represent the claim. Use it to write

H0 and Ha.

10. a) 𝑝 = 0.15

H0:

Ha:

11. b) 𝜇 < 125

H0:

Ha:

Sketch generally where the rejection regions would fall

based on the type of test (left/right/two-tailed).

12. For the claim, state the null and alternative hypothesis using

mathematical symbols.

Claim: a paint company claims the mean coverage of one gallon

of their paint is at least 400 ft2.

H0:

Ha:

Is this test left-tailed, right-tailed, or two-tailed?

13. An energy drink company claims their drinks have at least

215 mg of caffeine. As a quality control specialist, you test

this claim by sampling 60 drinks and find the mean is 212

mg with a population standard deviation of 8.4 mg.

a) Justify why we can use a normal approximation.

b) State each.

H0: Ha:

c) Calculate the test statistic.

d) Determine the p-value.

e) Make a decision and state your findings in context by

interpreting the p-value.

With a p-value of 0.003, we have strong evidence against the

null hypothesis and in favor of supporting the alternative claim

that this energy drink has less than 215 mg of caffeine.

Note: similar to the method shown in Problem 14, all of the

calculations for this could have been run by using the Z-Test

on the calculator with 𝝁𝟎 = 𝟐𝟏𝟓, 𝝈 = 𝟖. 𝟒, 𝒙 = 𝟐𝟏𝟐, 𝒏 =𝟔𝟎, and a left-tailed test.

14. A quality control specialist at Boeing is inspecting a sample

of a part that is supposed to have a weight of 55.2 grams.

The sample of 12 replications of that part has an average

weight of 55.3 grams with a sample standard deviation of

0.35 grams (assume a normally distributed population).

a) Justify whether to use a t or normal distribution.

Because we have a small sample (<30), we will use a t-

distribution.

b) State each.

H0: Ha:

c) Calculate the test statistic.

d) Determine the p-value.

e) Make a decision and state your findings in context by

interpreting the p-value.

With a p-value of 0.344, we have no evidence against the null

hypothesis and therefore fail to reject the null hypothesis that

the mean weight is 55.2 grams.

15. A university claims they accept on average at least 70% of

female applicants. In a random survey of 150 female

applicant records, it was found that 95 were accepted.

a) Justify why we can use a normal approximation.

b) State each.

H0: Ha:

c) Calculate the test statistic.

d) Determine the p-value.

e) Make a decision regarding the university’s claim and state

your findings in context by interpreting the p-value.

With a p-value of 0.037, we have moderate evidence against the

null hypothesis and in favor of supporting the alternative claim

that the university accepts less than 70% of female applicants.