Question

annie is concerned over a report that a woman over age 40 has a better chance of being killed by a terrorist than of getting married. a study found that the likelihood of marriage for a never-previously-wed, 40 -year-old university-educated american woman was 2.3% . to demonstrate that this percentage is too small, annie uses her resources at the baltimore sun to conduct a simple random sample of 476 never-previously-wed, university-educated, american women who were single at the beginning of their 40 s and who are now 45 . of these women, 16 report now being married. does this evidence support annies claim, at the 0.10 level of significance, that the chances of getting married for this group is greater than 2.3% ?

Answer 1

Annie's study found a marriage rate of about 3.36% among the sampled group, and by conducting a hypothesis test using the 0.10 level of significance, we can determine if this supports her claim that the marriage rate is greater than 2.3%.

Step-by-step explanation:

Annie is concerned about a statistic regarding marriage opportunities for never-previously-wed, university-educated American women over 40. A study claims that the likelihood of such a woman getting married is 2.3%. To refute this, Annie conducts her own research and finds that out of 476 similar women now aged 45, 16 are married. This yields an observed proportion of 16/476, which is about 3.36%. To determine if this evidence supports Annie's claim that the chances are greater than 2.3%, we can perform a hypothesis test.

For the hypothesis test, we will define the null hypothesis (H0) as the probability of marriage being 2.3% (p0 = 0.023) and the alternative hypothesis (H1) as the probability of marriage being greater than 2.3%. Using a 0.10 level of significance, we will calculate the test statistic and the corresponding p-value.

The formula for the test statistic in a proportion hypothesis test is:

z = (p - p0) / sqrt((p0(1 - p0)) / n)

where:
p is the sample proportion,
p0 is the hypothesized population proportion, and
n is the sample size.

Applying the sample data, we can calculate the test statistic and find the p-value using a z-table. If the p-value is less than 0.10, we reject the null hypothesis and conclude that there is evidence to support Annie's claim that the chance of getting married is greater than 2.3%.