Question

A movie company conducts a study to test the claim that the majority of people who watch their movies from 12:00-3:00 are all under 30. They surveyed 30 random people with a mean age of 28 years old, also the population standard deviation for the average viewer is 6 years. What can we conclude about their claim with 0.05 significance? Assume equal variances.

Answer 1

A movie company conducts a study to test the claim that the majority of people who watch their movies from 12:00-3:00 are all under 30.

They surveyed 30 random people with a mean age of 28 years old, also the population standard deviation for the average viewer is 6 years.

We Assume that the data are from normal population with mean μ and variance σ^2.

Here we want to test,

H0: μ = 30 versus H1: μ < 30

To test this our appropriate test statistic is given by,

t = ~ N(0, 1) under H0.

Where,

n = sample size = 30

σ = population Std Dev = 6

= sample mean = 28

= ​​​​​​​hypothesized mean = 30

t = = -1.8257

Note that, a small value of T indicates the rejection of H0, So a left tailed test based on t is appropriate. we reject H0 at significance level α = 0.05, if t < -τ_[α = 0.05].

Here we see that t = -1.8257 and -τ_[α = 0.05] = -1.645.

So, t = -1.8257 < -τ_[α = 0.05] = -1.645.

Hence we reject the null hypothesis H​​​​​​0​​​​​ at significance level α = 0.05 and we conclude that the claim of movie company is true that the mejority of people who watch their shows from noon to 3 pm are all under age 30.