Harvard University Independent Proportions Statistics Worksheet

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1. Research question about two independent proportions. What is the proportion of male and gemale students who noted for a student leader? 22 Data was obtained by randomly sampling 30 male students and 30 female students then ashed them whether they oted for a student leader or not. by interuening them. From the datos following information Gender. Male. Female. got the Sucross GES Failure (NO) 0,= 30 23 7 De= 30 17 13 Success (es) = This students who voted Failure ab) = Thors students who did not a student leader - note for a student leader. 3. Pick your own significance level and watter reative bopothesis ; Justify your choice. = 0.05 This show that I want to have 5% risk of concluding that a difference exists between the two proportions! when There is no actual difference between the two proportions! + Five step hypothesis test procedure. The proportion of make studente who voted for a student leader the same as proportion of gonale students who voted for a student leader H: The proportion of male students who voted for a student leader is different with proportion of gomale students who voted, for a student Step 2: Choose the statistical test to wo This is based on sample size. In this will be used caso, n=30 hence 2- test OS Successes SA Calculate proportions, P, and Pa basing number of sample size for each group. of makes who voted for a student leader. Total render of mates who students in the sample P = Number = 23 30 = 0.77 Number og females students who voted for a student leader. Total number of female students in the sample- 17 30 = 0.57 0,= 30 and no= 30. who do not of operation male vtudents and female students Nextcalaulate Note a For male studento; student leaders = 1-0.72 -0.23 For female students -1-0.57 = 0.43 as follows: Calculate the test statistic Zod 16) + Pa (2) na 0-77 - 0:57 0.77C6-R3) + 057(043) 30 30 23 0.1186 = 1.6863 p-value: CE sample statistic Calculate P-value is the probability of observing extreme as the test catetic We need to find the probability that the disperence in sample proportions in less than 0.2. This corresponds to the probability that a in less than 1.6863 2 1.69 This will be obtained from normal distribution table. Read the probability value that corresponds with P-value is 0.9545 But we want area to the legt, -0.9545 Multiply obtained value by a since this test is a two tailed test P-value = 0.0+55 XR 2 Score = 0.0455 = 0.091 P-value is greater than 0.05 level of significance. This shown that the result is not statistically insignificance. Fail to reject the oull bypothers and conclude that there is significant digeerence between the two proportions. no e copridense 5. State your Since this test is a = (1-x) 100. 61-0.05) 100 two-tailed test. confidence level will be: = 95% 6. Construct and interpret confidence interval. 95% confidence interval in = (P. - P) + 2y B (2) + Pi (2) x 2 = 1.00 from normal distribution table. 09 Pi 2 ni + 0.1186 14 D-R I 1.96 (0.1186) = 0.21 0:2 325 Upper Limit is; 0.2 +0.2325 -0.4325 Lower Limit is 0.2-0.2325 = -0.0 325 95% will be s (-0.0325, 0.4375) => (0, 41325). Here, replace the lower end poista by zero. We are 95% confident that population propation is between Odosas and 0.525 7. Since 95% confidence interval contains. statistically insignificant O then the test is
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1. Research question about two independent proportions.
What is the proportion of male and female students who voted for a student leader?
2. Data were obtained by randomly sampling 30 male students and 30 female students, then asking
them whether they voted for a student leader or not by interviewing them. From the data collection,
I got the following information.

Gender

n
Success
(Yes)
Failure (No)

Male

Female

n1=30

n2=30

23

17

7

13

Success (Yes): The students who voted for a student leader.
Failure (No): The students who did not vote for a student leader.
3. Pick your significance level α and alternative hypothesis; justify your choice.
α = 0.05
This shows that I want to have a 5% risk of concluding that a difference exists between the two
proportions where there is no actual difference between the two proportions.

4. Five-step hypothesis test procedure.
Step 1: Formulate the null and alternative hypotheses.
H0: The proportion of male students who voted for a student leader is the same as the proportion of
female students who voted for a student leader.
H1: The proportion of male students who voted for a student leader is different from the proportion
of female students who voted for a student leader.
Step 2: Choose the statistical test to use.
This is based on sample size. In this case, n=30 hence 2-test will be used.

Calculate proportions P1 and P1 based on the number of successes and sample size for e...


Anonymous
Awesome! Perfect study aid.

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