of 1000 respondents aged 2435 59 reported that they preferre

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.

Solution

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]