Question

Suppose you wish to test the hypothesis that the number of print media (newspaper, magazine, and so forth) that people subscribe to is related to subscribers’ education levels. The following hypothetical data was gathered form five people.

                                Number of subscriptions, x :4, 5, 1, 2, 3

Education level, y (years): 16, 20, 8, 9, 12

H0: The number of print media that people subscribe to is not related to subscribers’ education levels.

H1: The number of print media that people subscribe to is related to subscribers’ education levels.

Question: If the computed t value is in the rejection region (r=.97, p<.01), can you reject the null hypothesis at the p<.01 level of significance? Why? Show ALL work for the t-test calculation

Answer 1

Solution:

Here, we have to use t test for the population correlation coefficient. The null and alternative hypotheses for this test are given as below:

H₀: The number of print media that people subscribe to is not related to subscribers’ education levels.

H₁: The number of print media that people subscribe to is related to subscribers’ education levels.

H₀: ρ = 0 versus H₁: ρ ≠ 0

This is a two tailed test.

We are given level of significance = α = 0.01

The test statistic formula for this test is given as below:

t = r*sqrt(n – 2)/sqrt(1 – r^2)

From given data, we have

r = 0.980306

n = 5

df = n – 2 = 5 – 2 = 3

df = 3

α = 0.01

Critical values = -5.8409 and 5.8409

(by using t-table or excel)

t = r*sqrt(n – 2)/sqrt(1 – r^2)

t = 0.980306*sqrt(5 - 2)/sqrt(1 - 0.980306^2)

t = 0.980306*sqrt(3)/sqrt(0.039)

t = 8.597852

P-value = 0.003308

(by using t-table or excel)

P-value < α = 0.01

Test statistic value do not lies within Critical values -5.8409 and 5.8409.

So, we reject the null hypothesis

There is sufficient evidence to conclude that the number of print media that people subscribe to is related to subscribers’ education levels.