Question

A study conducted in September and October of 2010 found that fewer than half of employers who hired new college graduates last academic year plan to definitely do so again (The Wall Street Journal November 29, 2010) Suppose the hiring intentions of the respondents were as follows (Use Table 3) Definitely Hire Likely to Hire 179 Hire Uncertain 2896 will not Hire 18% Six months later, a sample of 500 employers were asked their hiring intentions and gave the following responses Definitely Hire 170 Likely to Hire 100 Hire Uncertain 120 Will not Hire 110 a. Choose the appropriate alternative hypothesis to test whether the proportions from the initial study have changed All population proportions differ from their hypothesized values At least one of the population proportions differs from its hypothesized value b. Find the critical value at the 5% significance level (Round your answer to 3 decimal places. Critical value c. Calculate the value of the test statistic (Round the intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Test statistic d. What is the conclusion to the hypothesis test? Reject Ho the proportions from the initial study have changed Reject Ho, the proportions from the initial study have not changed O Do not reject Ho the proportions from the initial study have changed Do not reject Ho the proportions from the initial study have not changed Type here to search

Answer 1

Solution:

A study conducted in September and October of 2010 found that fewer than haif of employers who hired new college graduates last academic year plan to definitely do so again (The Wall Street Journal November 29 2010) Suppose the hiring intentions of the respondents were as follows (Use Table 3) Definitely Hire 37% Likely to Hire 17% Hire Uncertain 28% Will not Hire 18% Six months later, a sample of 500 employers were asked their hiring intentions and gave the following responses Hire Uncertain Definitely Hire Likely to Hire 100 Will not Hire 110 170 120 (0-E) a. Choose the appropriate alternative hypothesis to test whether the proportions from the initial study have changed Observed Counts O Employers Definitely Hire Expected Counts E E Proportion All population proportions differ from their hunothesizod valuos At least one of the population proportions differs from its hypothesized value 0.37 170 185 1.22 Likely to Hire 0.17 100 85 2.65 b. Find the critical value at the 5 % significance level (Round your answer to 3 decimal places.) 2.86 Hire Uncertain 0.28 120 140 Will not Hire 0.18 110 90 4.44 Critical value 7.815 (О-Е) Σ E c. Calculate the value of the test statistic (Round the intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) = 11.16 500 500 Test statistic 11.16 11.16 d. What is the conclusion to the hypothesis test? Reject Ho the proportions from the initial study have changed Reject Ho. the proportions from the initial study have not changed Do not reject Ho the proportions from the initial study have changed Do not reject Hn the proportions from the initial study have not changed