Answer:
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).
