Question

Previously, an organization reported that teenagers spent of 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0.

Required:
Conduct a hypothesis test.

Answer 1

There is no significant evidence to conclude that the mean hours spent per week by teenagers is greater than 4.5

Explanation:

H0 : μ = 4.5

H1 : μ > 4.5

Sample size, n = 15 ; sample, mean, xbar = 4.75 ; sample Standard deviation, s = 2.0

Test statistic : (xbar - μ) ÷ s/sqrt(n)

Test statistic : (4.75 - 4.5) ÷ 2/sqrt(15)

Test statistic : 0.25 / 0.5163977

Test statistic = 0.484

Using the test statistic to obtain the Pvalue :

Using α = 0.05, df = 15 - 1 = 14

Pvalue = 0.3179

Since, Pvalue > α ; we fail to reject the Null.

We conclude that ;

There is no significant evidence to conclude that the mean hours spent per week by teenagers is greater than 4.5