14. Studies suggest that less than 1/3 of entering high school freshmen will end
ID: 3362212 • Letter: 1
Question
14. Studies suggest that less than 1/3 of entering high school freshmen will end up graduating school. Last years graduating class had a size of 115. There were 350 students in that group their freshman year. Test this hypothesis. -.05 Ho: P-value Ha: Reject or Fail to reject Ho? Conclusion: 15. A group of students were given a mathematics test. 25 out of the 35 women and 16 out of the 30 men passed. Did the women do better? Test the hypothesis. -.05 Ho: Ha: P-value Reject or Fail to reject Ho? Conclusion:Explanation / Answer
Solution:-
14) State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P > 0.3333
Alternative hypothesis: P < 0.3333
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected only if the sample proportion is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.
Analyze sample data. Using sample data, we calculate the standard deviation () and compute the z-score test statistic (z).
= sqrt[ P * ( 1 - P ) / n ]
= 0.0252
z = (p - P) /
z = - 0.19
where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.
Since we have a one-tailed test, the P-value is the probability that the z-score is less than - 0.19.
Thus, the P-value = 0.4247
Interpret results. Since the P-value (0.4247) is greater than the significance level (0.05), we have to accept the null hypothesis.
Fail to reject H0.
We do not have sufficient evidence in the favor of the claim that less than 1/3 of entering high school freshman ends up graduating school.
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