Question

1. A sample of 1000 people that live in a large city was asked if they believed that the city’s sales tax proposal was warranted. If at least two-thirds of the city’s citizens believe that the sales tax is warranted, then the mayor will take immediate steps to formally propose the tax. The survey responses showed that 692 of the 1000 people surveyed believe that the tax proposal is warranted.
   1. Write the appropriate null and alternative hypotheses for the one-tailed test that could be used to determine if this test provides statistically significant evidence that the proposal has the required level of support.
   2. Find the test statistic.
   3. Find the critical value for α=0.05.
   4. What is the result of the hypothesis test? Why?
   5. Find the critical value for α=0.1.
   6. What is the result of this hypothesis test? Why?
   7. Based on the results of (d) and (f), what range of values will the p-value be in? How do you know? Do not calculate the p-value to justify your answer.

Answer 1

Solution-A:

Ho:p>=2/3

Ha:p<2/3

Soluiton-B:

Z=p^-p/sqrt(p*(1-p)/n)

p^=x/n=692/1000=0.692

p=2/3=0.66667

z=(0.692-0.66667)/sqrt(0.66667*(1-0.66667)/1000)

z= 1.699192

Find the critical value for α=0.05.

critical value in excel is

=NORM.S.INV(0.05)

=-1.644853627

What is the result of the hypothesis test? Why?

1.699192>-1.644853627

Do not reject null hypothesis

Accept null hypothesis

Conclusion:

There is sufficient statistical evidence at 5% level of significance to conlcude that the proposal has the required level of support.