On September 21, 2022, the CDC announced that 40% of women in the United States were currently suffering from anxiety. Hoping that the proportion of women suffering from anxiety in her country was lower, Koko selected a random sample of 60 adult women from her country to find 22 of them suffering from anxiety. Does this provide evidence at the 8 % significance level of a lower proportion of women with anxiety in her county? Conduct the hypothesis test using a critical value approach. Select the correct answer.
Option A
The hypotheses are H0: p < 40%; Ha: p ≥ 40%; The test statistic is z = 0.8210. The p-value = 0.02084, do not reject Ho. Conclude the proportion of women in Koko’s country suffering from anxiety is significantly less than 40%.
Option B
The hypotheses are H0: p ≤ 40%; Ha: p > 40%; The test statistic is z = 0.7906. The p-value = 0.02146, reject Ho. Conclude the proportion of women in Koko’s country suffering from anxiety is significantly less than 40%.
Option C
The hypotheses are H0: p ≥ 40%; Ha: p < 40%; The test statistic is z = –0.7906. The p-value = 0.2146, do not reject Ho. Conclude the proportion of women in Koko’s country suffering from anxiety is not significantly less than 40%.
Option D
The hypotheses are H0: p ≥ 40%; Ha: p < 40%; The test statistic is z = –0.8210. The p-value = 0.2084, do not reject Ho. Conclude the proportion of women in Koko’s country suffering from anxiety is not significantly less than 40%.