We decline to reject the null hypothesis. There is not enough evidence to suggest that the observed test scores are significantly different from the expected test scores.
H_{0}: the distribution of disease cases follows the ethnicities of the general population of Santa Clara County.
Graph: Check student’s solution.
Decision: Reject the null hypothesis.
Reason for decision: pvalue < alpha
Conclusion: The makeup of cases does not fit the ethnicities of the general population of Santa Clara County.
Productuse Per Day  African American  Native Hawaiian  Latino  Japanese Americans  White  Totals 

1–10  9,886  2,745  12,831  8,378  7,650  41,490 
11–20  6,514  3,062  4,932  10,680  9,877  35,065 
21–30  1,671  1,419  1,406  4,715  6,062  15,273 
31+  759  788  800  2,305  3,970  8,622 
Totals  18,830  8,014  19,969  26,078  27,559  10,0450 
Product Use Per Day  African American  Native Hawaiian  Latino  Japanese Americans  White 

110  7,777.57  3,310.11  8,248.02  10,771.29  11,383.01 
1120  6,573.16  2797.52  6970.76  9,103.29  9,620.27 
2130  2,863.02  1,218.49  3,036.20  3,965.05  4,190.23 
31+  1,616.25  687.87  1,714.01  2,238.37  2,365.49 
 Reject the null hypothesis.
 pvalue < alpha
 There is sufficient evidence to conclude that product use is dependent on ethnic group.
Answers will vary. Sample answer: Tests of independence and tests for homogeneity both calculate the test statistic the same way $\sum}_{(ij)}\frac{{(OE)}^{2}}{E$. In addition, all values must be greater than or equal to five.
Marital Status  %  Expected Frequency 

Never Married  31.3%  125.2 
Married  56.1%  224.4 
Widowed  2.5%  10 
Divorced/Separated  10.1%  40.4 
 The data fit the distribution.
 The data do not fit the distribution.
 3
 chisquare distribution with df = 3
 19.27
 0.0002
 Check student’s solution.

 Alpha = 0.05
 Decision: Reject null hypothesis.
 Reason for decision: pvalue < alpha
 Conclusion: Data do not fit the distribution.
 H_{0}: The local results follow the distribution of the U.S. AP examinee population.
 H_{a}: The local results do not follow the distribution of the U.S. AP examinee population.
 df = 5
 chisquare distribution with df = 5
 chisquare test statistic = 13.4
 pvalue = 0.0199
 Check student’s solution.
 Alpha = 0.05
 Decision: Reject null when a = 0.05.
 Reason for decision: pvalue < alpha
 Conclusion: Local data do not fit the AP examinee distribution.
 Decision: Do not reject null when a = 0.01
 Conclusion: There is insufficient evidence to conclude that local data do not follow the distribution of the U.S. AP examinee distribution.
 H_{0}: The actual college majors of graduating females fit the distribution of their expected majors.
 H_{a}: The actual college majors of graduating females do not fit the distribution of their expected majors.
 df = 10
 chisquare distribution with df = 10
 test statistic = 11.48
 pvalue = 0.3211
 Check student’s solution.

 Alpha = 0.05
 Decision: Do not reject null hypothesis when a = 0.05 and a = 0.01.
 Reason for decision: pvalue > alpha
 Conclusion: There is insufficient evidence to conclude that the distribution of actual college majors of graduating females do not fit the distribution of their expected majors.
The hypotheses for the goodnessoffit test are:
 H_{0}: Surveyed obese fit the distribution of expected obese.
 H_{a}: Surveyed obese do not fit the distribution of expected obese.
Use a chisquare distribution with df = 4 to evaluate the data.
 The test statistic is χ^{2} = 9.85
 The pvalue = 0.0431
 At the 5% significance level, α = 0.05. For this data, p < α.
 At the 5% level of significance, from the data, there is sufficient evidence to conclude that the surveyed obese do not fit the distribution of expected obese.
 H_{0}: Car size is independent of family size.
 H_{a}: Car size is dependent on family size.
 df = 9
 chisquare distribution with df = 9
 test statistic = 15.8284
 pvalue = 0.0706
 Check student’s solution.

 Alpha: 0.05
 Decision: Do not reject the null hypothesis.
 Reason for decision: pvalue > alpha
 Conclusion: At the 5 percent significance level, there is insufficient evidence to conclude that car size and family size are dependent.
 H_{0}: Honeymoon locations are independent of bride’s age.
 H_{a}: Honeymoon locations are dependent on bride’s age.
 df = 9
 chisquare distribution with df = 9
 test statistic = 15.7027
 pvalue = 0.0734
 Check student’s solution.

 Alpha: 0.05
 Decision: Do not reject the null hypothesis.
 Reason for decision: pvalue > alpha
 Conclusion: At the 5 percent significance level, there is insufficient evidence to conclude that honeymoon location and bride age are dependent.
 H_{0}: The types of fries sold are independent of the location.
 H_{a}: The types of fries sold are dependent on the location.
 df = 6
 chisquare distribution with df = 6
 test statistic =18.8369
 pvalue = 0.0044
 Check student’s solution.

 Alpha: 0.05
 Decision: Reject the null hypothesis.
 Reason for decision: pvalue < alpha
 Conclusion: At the 5 percent significance level, there is sufficient evidence that types of fries and location are dependent.
 H_{0}: Salary is independent of level of education.
 H_{a}: Salary is dependent on level of education.
 df = 12
 chisquare distribution with df = 12
 test statistic = 255.7704
 pvalue = 0
 Check student’s solution.

Alpha: 0.05
Decision: Reject the null hypothesis.
Reason for decision: pvalue < alpha
Conclusion: At the 5 percent significance level, there is sufficient evidence to conclude that salary and level of education are dependent.
 H_{0}: Age is independent of the youngest online entrepreneurs’ net worth.
 H_{a}: Age is dependent on the net worth of the youngest online entrepreneurs.
 df = 2
 chisquare distribution with df = 2
 test statistic = 1.76
 pvalue = 0.4144
 Check student’s solution.

 Alpha: 0.05
 Decision: Do not reject the null hypothesis.
 Reason for decision: pvalue > alpha
 Conclusion: At the 5 percent significance level, there is insufficient evidence to conclude that age and net worth for the youngest online entrepreneurs are dependent.
 H_{0}: The distribution for personality types is the same for both majors.
 H_{a}: The distribution for personality types is not the same for both majors.
 df = 4
 chisquare with df = 4
 test statistic = 3.01
 pvalue = 0.5568
 Check student’s solution.

 Alpha: 0.05
 Decision: Do not reject the null hypothesis.
 Reason for decision: pvalue > alpha
 Conclusion: There is insufficient evidence to conclude that the distribution of personality types is different for business and social science majors.
 H_{0}: The distribution for fish caught is the same in Green Valley Lake and in Echo Lake.
 H_{a}: The distribution for fish caught is not the same in Green Valley Lake and in Echo Lake.
 3
 chisquare with df = 3
 11.75
 pvalue = 0.0083
 Check student’s solution.

 Alpha: 0.05
 Decision: Reject the null hypothesis.
 Reason for decision: pvalue < alpha
 Conclusion: There is evidence to conclude that the distribution of fish caught is different in Green Valley Lake and in Echo Lake.
 H_{0}: The distribution of average energy use in the United States is the same as in Europe between 2005 and 2010.
 H_{a}: The distribution of average energy use in the United States is not the same as in Europe between 2005 and 2010.
 df = 4
 chisquare with df = 4
 test statistic = 2.7434
 pvalue = 0.7395
 Check student’s solution.

 Alpha: 0.05
 Decision: Do not reject the null hypothesis.
 Reason for decision: pvalue > alpha
 Conclusion: At the 5 percent significance level, there is insufficient evidence to conclude that the average energy use values in the United States and EU are not derived from different distributions for the period from 2005 to 2010.
 H_{0}: The distribution for technology use is the same for community college students and university students.
 H_{a}: The distribution for technology use is not the same for community college students and university students.
 2
 chisquare with df = 2
 7.05
 p value = 0.0294
 Check student’s solution.

 Alpha: 0.05
 Decision: Reject the null hypothesis.
 Reason for decision: p value < alpha
 Conclusion: There is sufficient evidence to conclude that the distribution of technology use for statistics homework is not the same for statistics students at community colleges and at universities.
 H_{0}: σ = 15
 H_{a}: σ > 15
 df = 42
 chisquare with df = 42
 test statistic = 26.88
 pvalue = 0.9663
 Check student’s solution.

 Alpha = 0.05
 Decision: Do not reject null hypothesis.
 Reason for decision: pvalue > alpha
 Conclusion: There is insufficient evidence to conclude that the standard deviation is greater than 15.
 H_{0}: σ ≤ 3
 H_{a}: σ > 3
 df = 17
 chisquare distribution with df = 17
 test statistic = 28.73
 pvalue = 0.0371
 Check student’s solution.

 Alpha: 0.05
 Decision: Reject the null hypothesis.
 Reason for decision: pvalue < alpha
 Conclusion: There is sufficient evidence to conclude that the standard deviation is greater than three.
 H_{0}: σ = 2
 H_{a}: σ ≠ 2
 df = 14
 chisquare distiribution with df = 14
 chisquare test statistic = 5.2094
 pvalue = 0.0346
 Check student’s solution.

 Alpha = 0.05
 Decision: Reject the null hypothesis
 Reason for decision: pvalue < alpha
 Conclusion: There is sufficient evidence to conclude that the standard deviation is different than two.
The sample standard deviation is $34.29.
H_{0} : σ^{2} = 25^{2}
H_{a} : σ^{2} > 25^{2}
df = n – 1 = 7
Test statistic: ${x}^{2}={x}_{7}^{2}=\frac{(n\u20131){s}^{2}}{{25}^{2}}=\frac{(8\u20131){(34.29)}^{2}}{{25}^{2}}=13.169$;
pvalue: $P\left({x}_{7}^{2}>13.169\right)=1\u2013P\left({x}_{7}^{2}\le 13.169\right)=.0681$
Alpha: 0.05
Decision: Do not reject the null hypothesis.
Reason for decision: pvalue > alpha
Conclusion: At the 5 percent level, there is insufficient evidence to conclude that the variance is more than 625.
 The test statistic is always positive and if the expected and observed values are not close together, the test statistic is large and the null hypothesis will be rejected.
 Testing to see if the data fits the distribution too well or is too perfect.