# What are the null and alternate hypotheses?

The following output from MINITAB presents the results of a hypothesis test.

The following output from MINITAB presents.png”>

1.
What are the null and alternate
hypotheses?

2.
What is the value of the test
statistic?

3.
What is the P-value?

4.
Do you reject H0
at theThe following output from MINITAB presents.png”> level?

22.A
machine that fills beverage cans is supposed to put 12 ounces of beverage in
each can. Following are the amounts measured in a simple random sample of eight
cans.

·
11.96 12.10 12.04 12.13 11.98
12.05 11.91 12.03

1.
If appropriate, perform a
hypothesis test to determine whether the mean volume differs from 12 ounces.
Use theThe following output from MINITAB presents.png”> level of significance. What do you conclude?

20.Vertical
banded gastroplasty is a surgical procedure that reduces the volume of the
stomach in order to produce weight loss. In a recent study, 82 patients with
Type 2 diabetes underwent this procedure, and 59 of them experienced a recovery
from diabetes. Does this study provide convincing evidence that more than 60%
of those with diabetes who undergo this surgery will recover from diabetes? Use
theThe following output from MINITAB presents.png”>level of significance.

28.The
following MINITAB output presents the results of a hypothesis test for a
population proportion p.

The following output from MINITAB presents.png”>

1.
What are the null and alternate
hypotheses?

2.
What is the value of the sample
proportionThe following output from MINITAB presents.png”>?

3.
Can H0 be
rejected at the 0.05 level? Explain.

26.The
New York City Department of Health and Mental Hygiene conducts regular
inspections of restaurants. Each restaurant receives an inspection score, with
lower scores indicating a more satisfactory inspection. Following are scores
for the most recent inspection, as of October 2010, for random samples of 25
restaurants in the boroughs of Manhattan and Queens. Boxplots indicate that the
samples come from populations that are approximately normal.

Manhattan

2

22

23

0

40

12

37

43

27

15

24

8

38

4

17

21

11

18

13

30

27

19

38

21

4

Queens

27

18

14

20

35

8

42

29

0

12

25

0

19

6

13

22

5

11

0

10

19

39

2

8

19

Source: New York City Dept. of
Health and Mental Hygiene

Can you conclude that the mean
scores differ between the two boroughs? Use theThe following output from MINITAB presents.png”> level of significance.

28. The concentration of benzene was measured in
units of milligrams per liter for a simple random sample of five specimens of
untreated wastewater produced at a gas field. The sample mean was 7.8 with a
sample standard deviation of 1.4. Seven specimens of treated wastewater had an
average benzene concentration of 3.2 with a standard deviation of 1.7. It is
reasonable to assume that both samples come from populations that are
approximately normal. Construct a 99% confidence interval for the reduction in
benzene concentration after treatment.

36.The
following computer output (from MINITAB) presents the results of a hypothesis
test for the differenceThe following output from MINITAB presents.png”> between two population means:

The following output from MINITAB presents.png”>

1.
What is the alternate hypothesis?

2.
Can H0 be
rejected at theThe following output from MINITAB presents.png”> level? Explain.

3.
How many degrees of freedom are
there for the test statistic?

4.
Use the simpler method to compute
the degrees of freedom as the smaller ofThe following output from MINITAB presents.png”> andThe following output from MINITAB presents.png”>.

22.An
article in the Archives of Internal Medicine reported that in a sample
of 244 men, 73 had elevated total cholesterol levels (more than 200 milligrams
per deciliter). In a sample of 232 women, 44 had elevated cholesterol levels.
Can you conclude that the proportion of people with elevated cholesterol levels
differs between men and women? Use theThe following output from MINITAB presents.png”> level.

32.The
following computer output (from MINITAB) presents the results of a hypothesis
test on the difference between two proportions.

The following output from MINITAB presents.png”>

1.
Is this a left-tailed test, a
right-tailed test, or a two-tailed test?

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