Question

A report by the Gallup Poll found that a woman visits her doctor, on average, at most$5.8$times each year. A random sample of $20$women results in these yearly visit totals

$3;2;1;3;7;2;9;4;6;6;8;0;5;6;4;2;1;3;4;1$

At the α = 0.05 level can it be concluded that the sample mean is higher than $5.8$visits per year?

Short answer

There is insufficient evidence to conclude that the mean is higher than$5.8$visits per year.

Step-by-step solution

Given information 

Given that the average number of times a women visits her doctor is$5.8$

Explanation

In the right-tailed test, reject the null hypothesis if $p-value<0.05$.

The null hypothesis states that the mean number of visits per year is less than or equal to$5.8$

$H_0:\mu \le 5.8$

The alternative hypothesis suggests that the average number of visits per year is more than localid="1650624946822" $5.8$

$H_a:\mu >5.8$

Since the localid="1650464085153" $p-value=0.998$is greater than $0.05$. We can't conclude whether the sample mean is more than localid="1650624937866" $5.8$trips per year.