Question

While her husband spent $2½$hours picking out new speakers, a statistician decided to determine whether the percent of men who enjoy shopping for electronic equipment is higher than the percent of women who enjoy shopping for electronic equipment. The population was Saturday afternoon shoppers. Out of$67$men, $24$said they enjoyed the activity. Eight of the $24$ women surveyed claimed to enjoy the activity. We need to interpret the results of the survey .

Short answer

There is insufficient data to establish that the proportion of males who enjoy shopping for electronic equipment is greater than the proportion of women at the$5\%$ level of significance.

Step-by-step solution

Given information

Given in the question that, While her husband spent $2½$ hours picking out new speakers, a statistician decided to determine whether the percent of men who enjoy shopping for electronic equipment is higher than the percent of women who enjoy shopping for electronic equipment. The population was Saturday afternoon shoppers. Out of $67$ men, $24$said they enjoyed the activity. Eight of the $24$ women surveyed claimed to enjoy the activity. We need to interpret the results of the survey .

Explanation

a. The null hypothesis

$p_m\le p_w$

b. Alternative hypothesis

$p_m>p_w$.

c. The proportions of men and women are the random variable.

d. Two proportions with a normal distribution.

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

The result will be

$0.22$is the test statistics

f. The output has a $p$-value of $0.517$.

Graph

g .Graph the p-value matching region(s).

$\text{i.}\alpha =0.05$

ii. Conclusion: the null hypothesis should not be rejected.

iii. Justification for Decision:

$p-\text{value}<\alpha \text{.}$

iv. Conclusion: There is insufficient data to establish that the proportion of males who enjoy shopping for electronic equipment is greater than the proportion of women at the$5\%$level of significance.