of 1,000 respondents aged 24-35, 59% reported that they preferred to \"look for
ID: 3378410 • Letter: O
Question
of 1,000 respondents aged 24-35, 59% reported that they preferred to "look for a job in a place where I would like to live" rather than "look for the best job I can find, the place where I live is secondary." At the .01 level of significance, is there evidence that the proportion of all young job seekers aged 24-35 who preferred to "look for a job in the place where I would like to live" rather than "look for the best job I can find, the place where I live is secondary" different from 56%?
State the null and alternative hypothesis.
Calculate the Z stat.
What is the p value?
State the conclusion.
Explanation / Answer
Formulating the null and alternatuve hypotheses,
Ho: p = 0.56
Ha: p =/= 0.56 [ANSWER]
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As we see, the hypothesized po = 0.56
Getting the point estimate of p, p^,
p^ = x / n = 0.59
Getting the standard error of p^, sp,
sp = sqrt[po (1 - po)/n] = 0.015697133
Getting the z statistic,
z = (p^ - po)/sp = 1.911176968 [ANSWER, Z STAT]
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As this is a 2 tailed test, then, getting the p value,
p = 0.055981843 [ANSWER]
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significance level = 0.01
Comparing p >0.01, we FAIL TO REJECT THE NULL HYPOTHESIS.
There is no significant evidence that the proportion of all young job seekers aged 24-35 who preferred to "look for a job in the place where I would like to live" rather than "look for the best job I can find, the place where I live is secondary" is different from 56%. [CONCLUSION]
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