Previously, 10.1% of workers had a travel time to work of more than 60 minutes.

Question

Previously, 10.1% of workers had a travel time to work of more than 60 minutes. An urban economist believes that the percentage has increased since then. She randomly selects 95 workers find that 17 of them have a travel time to work is more than 60 minutes. Test the economist's belief at the a = 0.1 level of significance. Identify the null and alternative hypotheses. H_0:p 0.101 H_1: p 0.101 Use the to find the p-value Is there sufficient evidence to support the economist's belief? No, there is not sufficient evidence, because the P-value is greater than a, meaning that we do not reject the null hypothesis. Yes, there is sufficient evidence, because the P- value is less than a, meaning that we reject the null hypothesis No, there is not sufficient evidence, because the P- value is less than a, meaning that we reject the null hypothesis Yes, there is sufficient evidence because the P- value is greater than a, meaning that we do not reject the null hypothesis

Explanation / Answer

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   <=   0.101
Ha:   p   >   0.101

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As we see, the hypothesized po =   0.101      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.178947368      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.030915675      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    2.521289571      
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.005846279   [ANSWER, P VALUE]

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As P < 0.1, we reject Ho.

Hence, OPTION B. [ANSWER]

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