Question

1) Suppose that you wanted to know if the percentage of people who will attend a sporting event this year will decrease. Last year, 43% of Americans attended a sporting event. After taking a sample, you attain a sample percentage of 18% with a margin of error of 3%. Construct a confidence interval and use that interval to determine if the number of Americans who will attend a sporting event has decreased. Show your calculation for the interval and then state your conclusion in complete sentences.

Must show all work

Answer 1

Sol:

Ho:p=0.43

Ha:p<0.43

z critical value for 95%1=.96

95% confidence interal for p is

sample proportion-z*margin of error,sample proportion+z*margin of error

0.18-1.96*0.03,0.18+1.96*0.03

0.1212,0.2388

0.1212*100,,0.2388*100

12.12%,23.88%

95% lower limit for p=12.12%

95% upper limit for p=23.88%

since this 95% confidence interval range do not contain zero

Reject Ho

Accept Ha

Conclusion:

There is suffcient statistical evidence by 95% confidence interval that the percentage of people who will attend a sporting event this year decreased from 43%