Previously, an organization reported that teenagers spent 4.5 hours per week, on

Question

Previously, an organization reported that teenagers spent 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. Conduct a hypothesis test for each a,b,c,d. The null and alternative hypotheses are:

a. Ho: x = 4.5, Ha : x > 4.5

b. Ho: 4.5, Ha: < 4.5

c. Ho: = 4.75, Ha: > 4.75

d. Ho: = 4.5, Ha: > 4.5

Explanation / Answer

Here sample size = n = 15
sample mean = 4.75 hours, sample sd = 2 hours, population mean = 4.5 hours

Here the null hypothesis is - Ho: µ = 4.5 i.e. On average the teenagers spent 4.5 hours per week on phone
And alternative hypothesis is - Ha: µ > 4.5 i.e. On average the teenagers spent more than 4.5 hours per week on phone

This is one tailed t test.

Standard error = sd/sqrt(n) = 2/sqrt(15) = 0.5163978
Degrees of freedom = n - 1 = 15 - 1 = 14
t statistic = (4.75 - 4.5)/0.5163978 = 0.4841229

Taking significance level as 0.05
So critical probability = 1 - 0.05/2 = 0.975
Degrees of freedom = 14

Now Critical value of the test statistic can be found out using the t table, which is 2.145

Since the test statistic value 0.4841229 is less than the critical value of 2.145, we fail to reject the null hypothesis. So we can say that on average the teenagers spent 4.5 hours per week on phone

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