Variation in Sample Proportions (Example 7) Suppose it is known that 20 % of students at a certain college participate in a textbook recycling program each semester. a. If a random sample of 50 students is selected, do we expect that exactly 20 % of the sample participates in the textbook recycling program? Why or why not? b. Suppose we take a sample of 500 students and find the sample proportion participating in the recycling program. Which sample proportion do you think is more likely to be closer to 20 % : the proportion from a sample size of 50 or the proportion from a sample size of 500 ? Explain your reasoning.
Variation in Sample Proportions (Example 7) Suppose it is known that 20 % of students at a certain college participate in a textbook recycling program each semester. a. If a random sample of 50 students is selected, do we expect that exactly 20 % of the sample participates in the textbook recycling program? Why or why not? b. Suppose we take a sample of 500 students and find the sample proportion participating in the recycling program. Which sample proportion do you think is more likely to be closer to 20 % : the proportion from a sample size of 50 or the proportion from a sample size of 500 ? Explain your reasoning.
Solution Summary: The author determines whether a sample's proportion of participants in the book recycling program is equal to " 20% or not.
Variation in Sample Proportions (Example 7) Suppose it is known that
20
%
of students at a certain college participate in a textbook recycling program each semester.
a. If a random sample of 50 students is selected, do we expect that exactly
20
%
of the sample participates in the textbook recycling program? Why or why not?
b. Suppose we take a sample of 500 students and find the sample proportion participating in the recycling program. Which sample proportion do you think is more likely to be closer to
20
%
:
the proportion from a sample size of 50 or the proportion from a sample size of
500
?
Explain your reasoning.
Definition Definition Number of subjects or observations included in a study. A large sample size typically provides more reliable results and better representation of the population. As sample size and width of confidence interval are inversely related, if the sample size is increased, the width of the confidence interval decreases.
Question 2
The data below provides the battery life of thirty eight (38) motorcycle batteries.
100 83 83 105 110 81 114
99 101 105 78 115 74 96
106
89
94 81 106 91 93 86
79 103 94 108 113 100
117 120
77 93
93 85 76
89 78 88
680
a. Test the hypothesis that mean battery life is greater than 90. Use the 1% level of
significance.
b. Determine if the mean battery life is different from 80. Use the 10% level of
significance. Show all steps for the hypothesis test
c. Would your conlcusion in part (b) change at the 5% level of significance? |
d. Confirm test results in part (b) using JASP. Note: All JASP input files and output
tables should be provided
Suppose that 80% of athletes at a certain college graduate. You randomly select eight athletes. What’s the chance that at most 7 of them graduate?
Suppose that you flip a fair coin four times. What’s the chance of getting at least one head?
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