Harper’s Index claims that 23% of American are in favor of outlawing cigarettes. You decide to test this claim and ask a random sample of 200 Americans whether they are in favor of outlawing cigarettes. Out of 200 Americans, 54 are in favor. Use critical-value or p-value approach and a significance level of 0.05. Conduct a hypothesis test to determine whether there is enough evidence to reject the claim.

There is enough evidence not to reject the claim.

Step-by-step explanation:

H0: The population proportion of Americans in favor of cigarette outlawing is 0.23.

Ha: The population proportion of Americans in favor of cigarette outlawing is not 0.23.

Critical value approach

z = (p' - p) ÷ sqrt[p(1 - p) ÷ n]

p' is sample proportion = 54/200 = 0.27

p is population proportion = 23% = 0.23

n is number of Americans sampled = 200

z = (0.27 - 0.23) ÷ sqrt[0.23(1 - 0.23) ÷ 300] = 0.04 ÷ sqrt[8.855×10^-4] = 0.04 ÷ 0.0298 = 1.34

The test is a two-tailed test because the alternate hypothesis is expressed using not equal to.

Critical value at 0.05 significance level is 1.96

For a two-tailed test, the region of no rejection of H0 lies between -1.96 and 1.96

Conclusion:

Fail to reject H0 because the test statistic 1.34 falls within the region bounded by -1.96 and 1.96.

There is enough evidence not to reject the claim because the claim is contained in the null hypothesis (H0).