题目
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A jobs and recruitment company wants to determine the proportion of seniors in a Sydney university who enter the job market in a position directly related to their undergraduate field of study. In a sample consisting of 200 of the graduates from last year’s class, 132 have entered jobs related to their field of study. The career services director of the university has claimed that at least 70% of the university’s seniors enter the job market in a position directly related to their undergraduate field of Based on the above sample data, is there sufficient evidence that the proportion is less than 70%? Provide the answers to the following steps. Use a 5% level of significance to perform a Hypothesis test. 1. Ho: p (= ;; ) [Fill in the blank], ( Insert the correct sign from the bracket ) 2. Ha : p(< > ; > ; <) [Fill in the blank], ( Insert the correct sign from the bracket ) 3. Statistical test: (z / t) [Fill in the blank], test 4.Level of significance (be careful as to one-tailed or two-tailed) [Fill in the blank], 5.Set up critical values (Write the value in the box, include "-" sign if negative, if two values, just write the positive one) [Fill in the blank], 6.Gather sample data: P HAT = [Fill in the blank], ; n= [Fill in the blank], 7.Calculate test statistic (write your answer correct to 4 decimal places) [Fill in the blank], 8. Make statistical conclusion: (Reject / Do not reject) [Fill in the blank], the null hypothesis. There is (sufficient/insufficient) [Fill in the blank], evidence to rebut the director’s claim at 5% significance level.
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To begin, restate the scenario and the target parameters clearly: we have n = 200 graduates, with x = 132 entering jobs related to their field, so p-hat = x/n = 132/200 = 0.66. The university claims at least 70% do so (p ≥ 0.70), and we test whether the proportion is less than 0.70 using a 5% significance level.
Option 1 (Ho: p = 0.70 / Insert the correct sign): The null hypothesis for a one-sided test about whether the true proportion is less than 0.70 is p = 0.70. If we were testing whether p is exactly 0.70, this would be the neutral baseline, but for a one-sided test against p < 0.70 we still start from p = 0.70 as the boundary under H0. The equality sign ......Login to view full explanation登录即可查看完整答案
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