Chapter 10 Review
For each of these questions:
A) State the hypotheses.
B) Identify which hypothesis represents the claim.
C) Find the test statistic
D) State the rejection region
E) State whether or not you can support the claim (“Yes” or “No”)
1. A health care investigator wants to test the following claim: Of all people in the United
States, 16% had no health care visits in the previous year, 46% had 1-3 health care visits
in the previous year, 25% had 4-9 health care visits in the previous year, and 13% had 10
or more health care visits in the previous year. A random sample of people in the United
States finds that 99 people had no health care visits in the previous year, 376 people had
1 to 3 health care visits in the previous year, 167 people had 4-9 health care visits in the
previous year, and 92 people had 10 or more health care visits in the previous year. Test
the claim at α = 0.05.
2. The contingency table shows the educational attainment of a random sample of adults
in the United States by age in a recent year. Conduct a test for independence, using α =
0.10. Assume that the variables are independent.
25-44
45 and older
H.S. –
did not complete
H.S.
completed
College
1-3 years
College
4 or more years
556
964
1359
1941
1217
1389
1347
1488
The table shows the annual salaries of randomly selected teachers from three different
states.
1) Test the claim, at α = .10, that the variances of teacher salaries in California and Ohio
are the same.
a) State the hypotheses and identify the claim.
b)Find the test statistic.
c) Identify the p-value.
d)Can you support the claim?
2) Test the claim, at α = .05, that the mean annual salaries for teachers in the three
states are not the same.
a) State the hypotheses and identify the claim.
b)Find the test statistic.
c) Identify the p-value.
d)Can you support the claim?
Teacher Salaries
California
Ohio
Wyoming
60,645
45,300
37,300
50,622
46,400
58,022
41,400
42,650
36,800
59,000
58,025
32,440
46,150
64,800
42,250
63,200
41,200
35,600
68,400
44,980
44,600
53,400
50,425
52,934
1. A health care investigator wants to test the following claim: Of all people in the
United States, 16% had no health care visits in the previous year, 46% had 1-3
health care visits in the previous year, 25% had 4-9 health care visits in the
previous year, and 13% had 10 or more health care visits in the previous year. A
random sample of people in the United States finds that 99 people had no
health care visits in the previous year, 376 people had 1 to 3 health care visits
in the previous year, 167 people had 4-9 health care visits in the previous year,
and 92 people had 10 or more health care visits in the previous year. Test the
claim at α = 0.05.
A) 𝐻0 : The distribution of annual health care visits for adults living in the
United States is: zero annual health care visits, 16%; 1-3 annual
health care visits, 46%; 4-9 annual health care visits, 25%; 10 or
more annual health care visits, 13%.
𝐻𝑎 : The distribution of annual health care visits for adults living in the
United States differs from the percentages stated above.
B) The null hypothesis is the claim.
C) The test statistic is 𝛸 2 = 8.86
D) The rejection region is to the right of 7.815
E) NO – We reject the null, thus we also reject the claim.
2. The contingency table shows the educational attainment of a random sample of adults
in the United States by age in a recent year. Conduct a test for independence, using α =
0.10. Assume that the variables are independent.
H.S. –
did not complete
H.S.
completed
College
1-3 years
College
4 or more years
556
964
1359
1941
1217
1389
1347
1488
H.S. –
did not complete
H.S.
completed
College
1-3 years
College
4 or more years
25-44
663.49
1440.47
1137.54
1237.50
45 and older
856.51
1859.53
1468.46
1597.50
25-44
45 and older
A) 𝐻0 : The variables years of education attained and age are independent.
𝐻𝑎 : The variables years of education attained and age are dependent.
B) The null hypothesis is the claim.
C) The test statistic is 𝛸 2 = 66.182, and p = 2.877E-14
D) The rejection region is to the right of 6.251
E) NO – We reject the null, thus we also reject the claim.
The table shows the annual salaries of randomly selected teachers from three different
states.
1) Test the claim, at α = .10, that the variances of teacher salaries in California and Ohio
are the same.
a) State the hypotheses and identify the claim.
b)Find the test statistic.
c) Identify the p-value.
d)Can you support the claim?
Teacher Salaries
STAT – TEST – E (use Data, not Stats)
Ohio
Wyoming
L1, L2, and frequency for both set to 1, two-tailed California
60,645
45,300
37,300
𝐻0 : 𝑠12 = 𝑠22
𝐻𝑎 : 𝑠12 ≠ 𝑠22
50,622
46,400
58,022
(Claim)
41,400
42,650
36,800
𝐹 = 1.2299
𝑝 = .7918
Fail to Reject Null –
Variances in California and Ohio, at the
10% significance level, are the same.
59,000
58,025
32,440
46,150
64,800
42,250
63,200
41,200
35,600
68,400
44,980
44,600
53,400
50,425
52,934
The table shows the annual salaries of randomly selected teachers from three different
states.
2) Test the claim, at α = .05, that the mean annual salaries for teachers in the three
states are not the same.
a) State the hypotheses and identify the claim.
b)Find the test statistic.
c) Identify the p-value.
d)Can you support the claim?
Teacher Salaries
STAT – TEST – H (ANOVA)
L1,L2,L3
𝐻0 : 𝜇1 = 𝜇2 = 𝜇3
𝐻𝑎 : At least one mean is different (Claim)
𝐹 = 4.3118
𝑝 = .027
Reject Null –
At the 5% significance level, there is enough
evidence to conclude that at least one
of the means is different from the others.
California
Ohio
Wyoming
60,645
45,300
37,300
50,622
46,400
58,022
41,400
42,650
36,800
59,000
58,025
32,440
46,150
64,800
42,250
63,200
41,200
35,600
68,400
44,980
44,600
53,400
50,425
52,934