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UNIT 6 REVIEW STATISTICAL TESTING
1. A company claims that their dishwashers last an average of 8 years with a standard deviation of 2.5 years. You have tested 40 of these dishwashers and find that the average is 7.2 years. Is this difference statistically significant at a 95% level?
a. State the hypotheses.
b. Choose the appropriate test. Why did you choose this test?
c. Find the p value. What does this mean?
d. State your conclusion.
2. In a study of OHS students I.Q., you find that 20 randomly chosen females have an average of 112 with a standard deviation of 15. 40 randomly chosen males have an average of 105 with a standard deviation of 20. Is there a significant difference between the average I.Q. of boys and girls at OHS?
a. State the hypotheses.
b. Choose the appropriate test. Why did you choose this test?
c. Find the p value. What does this mean?
d. State your conclusion.
3. In a survey of teaching effectiveness, 30 out of 42 students feel that Mr. Ebert is an effective teacher. 33 out of 57 parents of students feel that Mr. Ebert is an effective teacher. Are the proportion of students and parents different at a 95% significance level?
a. State the hypotheses.
b. Choose the appropriate test. Why did you choose this test?
c. Find the p value. What does this mean?
d. State your conclusion.
4. A national study finds that 24% of all high school students have tried marijuana. At OHS, a study finds that 10 out of 38 randomly selected students have tried marijuana. Is the proportion of OHS students who have tried marijuana different than the national proportion at a 95% significance level?
a. State the hypotheses.
b. Choose the appropriate test. Why did you choose this test?
c. Find the p value. What does this mean?
d. State your conclusion.
5. In a study of OHS students, 100 freshmen were randomly selected. They reported that they skipped an average of 8 classes with a standard deviation of 4.2. 75 seniors were randomly selected and reported that they skipped an average of 5.3 classes with a standard deviation of 2.9. Is the average number of times freshmen skip class significantly different than the average number of times seniors skip class?
a. State the hypotheses.
b. Choose the appropriate test. Why did you choose this test?
c. Find the p value. What does this mean?
d. State your conclusion.
6. Consumers preferences for five brands of chocolate are below. Is there
significant variation among peoples preferences?
BrandABCDE#1411201317
a. State the hypotheses.
b. Choose the appropriate test. Why did you choose this test?
c. Calculate the test statistic.
d. What is the value from the table?
e. State your conclusion.
7. A national study finds that 48% of all high school students attend religious worship services. At OHS, 52 out of 80 randomly selected students attend religious worship services. Is this different from the national proportion at a 95% level of significance?
a. State the hypotheses.
b. Choose the appropriate test. Why did you choose this test?
c. Find the p value. What does this mean?
d. State your conclusion.
8. A study in chemistry class finds that the average freezing temperature of 25 mixtures is 19( F with a standard deviation of 8(. The theoretical freezing temperature of this mixture is 23.4(. Are the observed results significantly different that this theoretical value?
a. State the hypotheses.
b. Choose the appropriate test. Why did you choose this test?
c. Find the p value. What does this mean?
d. State your conclusion.
9. You are studying the athletic ability of students in different sports. The average 40m dash times of 20 soccer players is 4.9 seconds with a standard deviation of 1.2. The average 40m dash times of 25 basketball players is 5.2 seconds with a standard deviation of 0.9. Are the average 40m dash times of soccer and basketball players significantly different at a 95% level?
a. State the hypotheses.
b. Choose the appropriate test. Why did you choose this test?
c. Find the p value. What does this mean?
d. State your conclusion.
10. In the Statistics Olympics, students are asked to determine how many M&Ms they can catch in their mouth out of ten that they toss in the air. For the 47 females, the average is 5.3 with a standard deviation of 2.8. For the 38 males, the average is 7.1 with a standard deviation of 3.3. Is the average number that females can catch significantly different than the average number that males can catch?
a. State the hypotheses.
b. Choose the appropriate test. Why did you choose this test?
c. Find the p value. What does this mean?
d. State your conclusion.
11. The average GPA of all high school students nationwide is 3.0 with a standard deviation of 0.8. At OHS, 50 random students have an average GPA of 2.85. Is the average GPA of students at OHS significantly different that the national average?
a. State the hypotheses.
b. Choose the appropriate test. Why did you choose this test?
c. Find the p value. What does this mean?
d. State your conclusion.
12. The number of students in different study halls is shown in the table below. Is there a significant variation among class periods?
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a. State the hypotheses.
b. Choose the appropriate test. Why did you choose this test?
c. Calculate the test statistic.
d. What is the value from the table?
e. State your conclusion.
UNIT 6 REVIEW SOLUTIONS
1. a. H0: ( = 8
HA: ( `" 8
b. z test
comparing the mean of a sample to a set number
c. p ( .043
the probability of the null hypothesis being true is .043.
d. reject H0
2. a. H0: (f = (m
HA: (f `" (m
b. 2 sample t test
comparing the means of two samples
c. p ( .135
the probability of the null hypothesis being true is .135.
d. do not reject H0
3. a. H0: ps = pp
HA: ps `" pp
b. 2 proportion z test
comparing the proportions of two samples
c. p ( .167
the probability of the null hypothesis being true is .167.
d. do not reject H0
4. a. H0: p = .24
HA: p `" .24
b. 1 proportion z test
comparing the proportion of a sample to a set proportion
c. p ( .738
the probability of the null hypothesis being true is .738.
d. do not reject H0
5. a. H0: (f = (s
HA: (f `" (s
b. 2 sample z test
comparing the means of two samples
c. p ( .0000005
the probability of the null hypothesis being true is .0000005.
d. reject H0
6. a. H0: variation is caused by
chance
HA: there is variation
b. (2 test
comparing variation
c. 3.333
d. 9.488
e. do not reject H0
7. a. H0: p = .48
HA: p `" .48
b. 1 proportion z test
comparing the proportion of a sample to a ? ?
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c. p ( .002
the probability of the null hypothesis being true is .002.
d. reject H0
8. a. H0: ( = 23.4
HA: ( `" 23.4
b. t test
comparing the mean of a sample to a set number
c. p ( .011
the probability of the null hypothesis being true is .011.
d. reject H0
9. a. H0: (s = (b
HA: (s `" (b
b. 2 sample t test
comparing the means of two samples
c. p ( .36
the probability of the null hypothesis being true is .36.
d. do not reject H0
10. a. H0: (f = (m
HA: (f `" (m
b. 2 samTTTTTTTUU,UUUUVV8V:VVbV~VVVVgd9^gd@0^`0gd@gd@^gd@0^`0gd@UUU UUUUUUUV4V6VJVLVNVRVTVVV\V^V`VhVjVnVpVrVxVzVV~VVVVVVVVVVVVW4WtWWWWWWWWWWWWWWWWWWWWWWWصصذŨصŨصhV=9h9H* h96 jmhV=9h96 h9H* jmh@h96h@h9H*h9h@h@H* jh@h@h@6 hV=96h@hV=9BVVWxWWWWWWWWWW`\`^`x```aaa8aTagd@gd9^gd@^gd@0^`0gd@0^`0gd@ple z test
comparing the means of two samples
c. p ( .0075
the probability of the null hypothesis being true is .0075.
d. reject H0
11. a. H0: ( = 3.0
HA: ( `" 3.0
b. z test
comparing the mean of a sample to a set number
c. p ( .185
the probabilityWX``
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aa"a$a(a*a6a>a@aDaFaRa\a^aaaaaabh h*h1h8h@hAhIhMhNhPhZhyhzh}h~hhhhhhhhhhhh@h@hV=9h9H* jch96hV=9h9h@h9H* jmh@h@6h@h@H* jh@h@h@6h@ h@6Uh9;TaVajaaaa,h.hBhChDhEhshzhhhhh^gd90^`0gd9gd9^`gd90^`0gd9^gd@0^`0gd@^gd@0^`0gd@gd@ of the null hypothesis being true is .185.
d. do not reject H0
12. a. H0: variation is caused by
chance
HA: there is variation
b. (2 test
comparing variation
c. 18.133
d. 15.507
e. reject H0
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