Question

A group of friends debated whether more men use smartphones than women. They consulted a research study of smartphone use among adults. The results of the survey indicate that of the 973 men randomly sampled, 379 use smartphones. For women, 404 of the 1,304 who were randomly sampled use smartphones. Test at the 5% level of significance.

a) More men use smartphones than women.

b) More women use smartphones than men.

c) Both a,b,and c

d) None of the above

Answer 1

To determine if more men use smartphones than women, we can use a hypothesis test. We set up the null and alternative hypotheses, calculate the proportions, standard error, and test statistic, and compare the test statistic to the critical value. Since the test statistic is greater than the critical value, we reject the null hypothesis and conclude that more men use smartphones than women.

Step-by-step explanation:

To determine if more men use smartphones than women, we can use a hypothesis test. Let's set up the null and alternative hypotheses:

Null Hypothesis (H0): The proportion of men using smartphones is equal to the proportion of women using smartphones.

Alternative Hypothesis (Ha): The proportion of men using smartphones is greater than the proportion of women using smartphones.

We will perform a two-proportion z-test at a 5% significance level to test these hypotheses. First, we calculate the proportions of men and women using smartphones:

Proportion of men using smartphones: 379/973 = 0.3899 (rounded to four decimal places)

Proportion of women using smartphones: 404/1304 = 0.3098 (rounded to four decimal places)

Next, we calculate the standard error:

Standard error: sqrt( (0.3899 * (1-0.3899))/973 + (0.3098 * (1-0.3098))/1304 ) = 0.0191 (rounded to four decimal places)

Finally, we calculate the test statistic:

Test statistic: (0.3899 - 0.3098) / 0.0191 = 4.1958 (rounded to four decimal places)

Consulting the z-table, we find that the critical value for a one-sided test at a 5% significance level is approximately 1.645. Since the test statistic (4.1958) is greater than the critical value (1.645), we reject the null hypothesis.

Therefore, we can conclude that there is sufficient evidence to suggest that more men use smartphones than women.