AP Statistics
Review: Hypothesis Testing
Part I. Answer the following
Name_________________
1.
A company manager says that the mean number of items produced per shift is 145 with a standard deviation of 8. The supervisor believes each shift produces more than 145 items. In a sample of 35 shifts, the mean number of items produces was
150. Does each shift produce more than 145 items? a.
Give the hypotheses b.
Describe a Type I error & its consequences. c.
Describe a Type II error & its consequences
2.
If a type II error is considered worse than a type I, would you use a 1% significance level or a 10% significance level? Explain.
3.
What are the hypotheses?
4.
We always reject or fail to reject the ______________ and support or fail to support the ______________.
5.
The probability of a Type I error is called the ____________________ and is represented by ___________.
6.
Explain why we reject the null hypothesis when the p-value is extremely small.
7.
Do we ever prove that the null hypothesis is really true? Explain.
8.
When do we use a t-test for means?
9.
If we are performing a one-tailed (right) large sample z-test with a calculated z

2.56
, then what is the P-value? What if it was a two-tailed test.
10.
Explain the p-value.

Part II. Do the following hypothesis tests.
11.
A consumer tested 38 bottles of a soft drink and found a sample mean of 15.8 ounces. The standard deviation is known to be 0.5 ounces. The bottles are supposed to contain at least 16 ounces, can we conclude that they actually contain less? Use  = 0.05.
12.
A magazine stated that 75% of all teenage boys have their own radios. A researcher wished to test the claim and selected a random sample of 60 teenage boys. She found that 54 had their own radios.
At  = 0.01, can the researcher conclude that the proportion of teenage boys who have their own radios is no longer 75%?
13.
A sociologist wishes to see if it is true that for a certain group of professional women, the average age at which they have heir first baby is 28.6. The sociologist selects a sample of 26 women and finds their mean age for first giving birth was 29.2 and a standard deviation of 3.1 years. At  = 0.10, can she conclude that the mean age at which a professional woman has her first baby is not 28.6?

14.
A dietitian read in a survey that at least 55% of adults do not eat breakfast at least three days a week. To verify this, she selected a random sample of 80 adults and asked them how many days a week they skipped breakfast. A total of 50% responded that they skipped breakfast at least three days a week. At  = 0.10, can we conclude that it is actually less than 55% of adults who do not eat breakfast at least three days a week?
15.
A manager states that in his factory, the average number of days per year missed by the employees due to illness is less than the national average of 10. The following data show the number of days missed by 24 employees last year. Is there sufficient evidence to believe the manager's statement at
 = 0.05?
0
3
7
6
9
4
12
6
7
3
0
1
3
7
0
5
6
8
4
4
12
1
3
3

Part III. Review of Old Material.
16. Harley-Davidson motorcycles make up 14% of all the motorcycles registered in the United States. You plan to interview an SRS of 500 motorcycle owners. What’s the probability that 20% or more own
Harleys?
17. A study found that 48 out of the 200 students surveyed had cheated on a test. Calculate a 90% confidence interval for the true proportion of student who have cheated on a test.
18. Approximately 82% of all students have copied a classmate’s homework. I have a class of 32. a.
How many do you expect to find have copied? b.
What is the probability that exactly 28 have copied? c.
What is the probability that at least 25 have copied? d.
What is the probability that less than 21 have copied?
19. The number of flaws per square yard in a type of carpet material varies with a mean of 1.8 flaws per square yard and st. dev. 1.2 flaws. An inspector studies 200 square yards, what the probability that the mean number of flaws exceeds 2 per square yard?

20. The probability that Ed hits the ball when he goes to bat is 0.23. Find the probability that he doesn’t get a hit until his 3 rd time at bat.
21. If I want to estimate the mean SAT score within 5 points with a 99% confidence, how large of a sample would you need. The standard deviation is 100.
22. The composition of the earth’s atmosphere may have changed over time. The gas in bubbles within amber should be a sample of the atmosphere at the time the amber was formed. The measures on specimens of amber are shown below. Construct and interpret a 95% confidence interval for the mean percent of nitrogen in ancient air.
63.4 65 64.4 63.3 54.8 64.5 60.8
23. Find the mean and standard deviation of the following:
20
0.02
25
0.03
30
0.08
35
0.12 x p(x)
40
0.22
45 50
0.28
24. I want to test my sweet pea seeds to determine the germination rate, that is the percent of seeds that sprout. How large of a sample of seeds will I need to be within 4% of the true proportion?