Question

Random samples of players for two types of video games were selected, and the mean number of hours per week spent playing the games was calculated for each group. The sample means were used to construct the 90 percent confidence interval (1.5, 3.8) for the difference in the mean number of hours per week spent playing the games. The maker of one of the video games claims that there is a difference in the population mean number of hours per week spent playing the two games . Is the claim supported by the interval? see pictures for answers

A) Yes, because 0 is not contained in the interval. Yes, because the midpoint of the interval is greater than 1. C) Yes, because the margin of error for the estimate is less than 1. D) No, because the margin of error for the estimate is greater than 1. E ) No, because 0 is not contained in the interval.

Answer 1

Solution:

Answer is

Yes , because 0 is not contained in the interval.

1st option is correct.

Explanation :

Given interval for the difference between two means is (1.5 , 3.8)

Claim: there is a difference in the population mean number of hours per week spent playing the two games

i.e. $\mu_{1}$   $\neq$$\mu_{2}$

Null and alternative hypothesis are

H₀: $\mu_{1}$ =  $\mu_{2}$ vs H₁ : $\mu_{1}$   $\neq$$\mu_{2}$

i.e.

H₀: $\mu_{1}$ - $\mu_{2}$ = 0 vs H₁ : $\mu_{1}$ - $\mu_{2}$ $\neq$ 0

Observe the interval . 0 in not in the interval.

So we reject H₀.

There is a difference in the population means.

So answer is

Yes , because 0 is not contained in the interval.

1st option is correct.