Question

On average, Canadians watch 21.4 hours of television per week. A sociologist claims that TV viewers in Quebec differ from the Canadian national average. A random sample of 35 Quebec households during a one-week period had a mean of 23.3 hours per week. A previous report showed population standard deviation to be 3.2 hours per week. Is there sufficient evidence at the 0.01 level of significance that the average weekly television viewing hours for Quebecers differs from the national average of all Canadians?

Answer 1

Here our hypothesis is,

H₀: vs H₁: where is the average viewers in Quebec. Here we have sample of 35 Quebec households with a mean = 23.3 and the population sd is 3.2.

Our test statistic is,

which follow N(0,1) under the null hypothesis.

So, here Z = 3.512672.

Now, the critical value of the test is upper 0.5% point of N(0,1) i.e. 2.575829.

Now, here the absolute value of the test statistic is 3.512672 which is greater than the critical value. So, we can reject the null hypothesis at 1% level of significance. So, we have sufficient evidence at 1% level of significance to conclude that the average weekly television viewing hours for Quebecers differs from the national average of all Canadians.