Question

In 2013, the Gallup Poll asked 1031 U.S. adults whether they believed that people should pay sales tax on items purchased over the internet. Of these, 443 said they supported such a tax. Does the survey provide convincing evidence that less than 45% of U.S. adults favor an internet sales tax? Use the α=0.05 level of significance and the P-value method with the TI-84 Plus calculator.

a. state null and alternative hypothesis. what tail is the hypothesis test?

b. Compute the value of the test statistic.

c. Using α=0.05, can you conclude that less than 44% of U.S. adults favor an internet sales tax?

d. state conclusion

Answer 1

Null hypothesis:

The proportion of US adults  believed that people should pay sales tax on items purchased over the internet is 45

H0: p = 0.45

Alternate hypothesis:

The proportion of US adults  believed that people should pay sales tax on items purchased over the internet is less than 45

H1: p < 0.45

Z = -1.3115

At α=0.05, z_c = -1.645 for left tailed

Reject H0, if Z < z_c

Here, Z = -1.3115 > z_c = 1.645

hence, we do not reject the null hypothesis

The proportion of US adults  believed that people should pay sales tax on items purchased over the internet is 45