Question

A survey of 700 adults from a certain region​ asked, "What do you buy from your mobile​ device?" The results indicated that 53​% of the females and ​44% of the males answered clothes. The sample sizes of males and females were not provided. Suppose that of 300​females, 159 reported they buy clothing from their mobile​ device, while of 400 ​males, 176 reported they buy clothing from their mobile device.

Is there evidence of a difference between males and females in the proportion who said they buy clothing from their mobile device at the 0.03 level of​ significance?

What is the statistical decision resulted from performing an appropriate hypothesis test?

Answer 1

To test for a difference between males and females in the proportion who buy clothing from their mobile device, we can use a hypothesis test. Calculate the sample proportions for both males and females, calculate the standard error of the difference between the proportions, and compare the test statistic to the critical value.

Step-by-step explanation:

To test whether there is a difference between males and females in the proportion who said they buy clothing from their mobile device, we can use a hypothesis test. The null hypothesis (H0) is that there is no difference between the proportions for males and females, and the alternative hypothesis (Ha) is that there is a difference.

1. Calculate the sample proportions for both males and females. For females, the proportion is 159/300 = 0.53. For males, the proportion is 176/400 = 0.44.
2. Calculate the standard error of the difference between the proportions using the formula: SE = sqrt(p1 * (1 - p1) / n1 + p2 * (1 - p2) / n2), where p1 and p2 are the sample proportions and n1 and n2 are the sample sizes.
3. Calculate the test statistic, which is the difference between the sample proportions divided by the standard error.
4. Find the critical value for the test statistic at the 0.03 level of significance.
5. Compare the test statistic to the critical value. If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that there is evidence of a difference between males and females in the proportion who said they buy clothing from their mobile device. If the test statistic is less than the critical value, we fail to reject the null hypothesis.