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.

Short answer

At the $5\%$level of significance, men are more likely than women to use smart phones.

Step-by-step solution

Given information

Given in the question that, 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. We need to test it at the $5\%$level of significance.

Explanation

a. The null hypothesis is defined as

$p_m\le p_w$

b. An alternative hypothesis is,

$p_m>p_w$

c. The random variable is the difference between male and female proportions.

d. Two proportions have a normal distribution.

e. Fill in all requirements using Minitab's two sample t test option.

The result will be

Test results statistics 3.94

f. The output has a p-value of $0.00$.

g. Because the value of $p$is 0, no graph is required.

i. $\alpha =0.05\$$

ii. Decision: the null hypothesis is rejected.

iii. $p$- value $\alpha$is the reason for the decision.

iv. Conclusion: At the $5\%$level of significance, men are more likely than women to use smart phones.