Question

Statistics Canada did a survey of Canadians in 2018 and determined that the average adult female over the age of 18 watches 25.6 hours of television per week while the average male watches 20.9 hours per week. Suppose that the sample comprised 35 females and 50 males (obviously the real samples were much larger) and that the sample standard deviations were 7.2 hours for females and 7 hours for males.

a) [4 marks] Is there sufficient evidence, at the 5% significance level, to show that adult women spend more time watching TV than adult men? Assume equal variances and a pooled standard deviation of 7.08.

b) [2 marks] Calculate the appropriate confidence interval to confirm the conclusion from part a). Does this confidence interval confirm your conclusion from part (a)? Explain.

c) [2 marks] Suppose you were more concerned with detecting a real difference than worrying about attributing a difference when there is none. In this case, would a significance level of 0.10 or 0.01 be more appropriate?

Answer 1

given =25.6

=20.9

=7.08

n1=35

n2=50

Let and be the average time spend by an adult women and an adult men respectively

To test

Ho:=

H1:>

The test statistic is given by

under Ho this reduces to

Now as the degree of freedom is given by n1+n2-2=35+50-2=83 and table value for 83 degree of freedom is not available normal approximation is used.

As degree of freedom is quite high normal approximation can be used

Hence

P(Z>3.01215)=0.0013

as 0.0013<0.05 reject Ho at 5%.

Hence we have enough evidence to claim that the average number of television hour per week is higher for women than men.

b) confidence interval is given by

Here 1.64 is the table value of standard z variate above which the probability is 0.05 as given alpha is 0.05

hence this is the required confidence interval

Yes, This confidence interval confirm my conclusion from part A.

c) in this case my significance level of 0.01 would be more appropriate because my type 1 error that is probability of rejecting Ho given Ho is true would be less and i would arrive at the better conclusion, that is i would be capturing the real difference more accurately.