The unemployment rate for 18 to 34 year olds was reported to

The unemployment rate for 18 to 34 year olds was reported to be 10.8% (The Cincinnati Enquirer, November 6, 2012). Assume that this report was based on a random sample of 400 18 to 34 year olds.

a. A political campaign manager wants to know if the sample results can be used to conclude that the unemployment rate for individuals 18 to 34 years old is significantly higher than the unemployment rate for all adults. According to the Bureau of Labor Statistics the unemployment rate for all adults was 7.9%. Develop a hypothesis test that can be used to see if the conclusion that the unemployment rate is higher for 18 to 34 year olds can be supported.
H0: p - Select your answer -greater than or equal to .079greater than .079less than or equal to .079less than .079equal to .079not equal to .079Item 1
Ha: p - Select your answer -greater than or equal to .079greater than .079less than or equal to .079less than .079equal to .079not equal to .079Item 2

b. Use the sample data collected for the 18 to 34 year olds to compute the p-value for the hypothesis test in part (a) (to 4 decimals).

Using =.05, what is your conclusion?
- Select your answer -The unemployment rate for 18 to 34 year olds is significantly higher than the national unemployment rate of 7.9% for all adults.The unemployment rate for 18 to 34 year olds is significantly lesser than the national unemployment rate of 7.9% for all adults.Item 4

c. Explain to the campaign manager what can be said about the observed level of significance for the hypothesis testing results using the p-value.

Solution

a)

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   <=   0.079
Ha:   p   >   0.079 [ANSWER]

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b)

As we see, the hypothesized po =   0.079      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.108      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.013486938      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    2.150228594      
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.015768569   [ANSWER, P VALUE]
  
significance level =    0.05      

As P < 0.05, we REJECT THE NULL HYPOTHESIS.   [ANSWER]

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c)

If the proportion of 18-34 year old unemployed are not significantly higher than all adults, then there is only around 1.58% chance of this kind of experiment happening. Since, we treat 5% as rare enough so that we don\'t believe it is simply by chance, then we say that the proportion really is significantly greater than 0.079.