According to the video game industry's statistics, the average gamer is 34 years old. Imagine the standard deviation for age is 7.5 years. Leroy collected data on video gaming among people with new tablets or iPads to see if the mean age of that group is older or younger. He finds an average age of 36 years based on a sample size of 48. His 95 percent confidence interval is:

lower range 33.822 years

upper range 38.178 years

Explanation:

step 1:

48 - 1 = 47

step 2:

(1 - 95%) / 2 = 0.025

step 3:

we look at the T distribution table for degrees of freedom (df) = 47, and α = 0.025; = 2.0117

step 4:

divide sample standard deviation by square root of sample size

7.5 years / √48 = 7.5 / 6.9282 = 1.0825

step 5:

multiply results from step 3 and 4

2.0117 x 1.0825 = 2.178

step 6:

for the lower range, subtract step 5 from sample mean

36 - 2.178 = 33.822

step 7: for the upper range, add step 5 with sample mean

36 + 2.178 = 38.178