Question

Questions 7 – 17. A researcher is interested in whether New Yorkers watch more TV than theaverage American. In the population, Americans watch an average of 34 hours of TV per week. A researcher surveys 28 New Yorkers and finds that they watch an average of 32 hours of TV per week with a variance of 25. The researcher uses an alpha level of 0.01.

7. Is this a one- or two-tailed test?

8. What is the null hypothesis?

9. What is the alternative hypothesis?

10. What are the degrees of freedom?

11. What is t critical?

12. What is the standard error?

13. What is the t statistic (t obtained)?

14. What decision would you make about H0?

15. What can you conclude?

16. What is the effect size?

17. What does this effect size mean?

Answer 1

7)

It is one tailed test

8)

H0 :- µ = 34

9)

H1 :- µ > 34

10)

Degree of freedom = n - 1 = 28 - 1 = 27

11)

Critical value t(α, n-1) = t(0.01 , 28-1) = 2.473

12)

Standard Error = S/√(n) = 0.9449

13)

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 32 - 34 ) / ( 5 / √(28) )
t = -2.1166

14)

Test Criteria :-
Reject null hypothesis if t > t(α, n-1)
Critical value t(α, n-1) = t(0.01 , 28-1) = 2.473
t > t(α, n-1) = -2.1166 < 2.473
Result :- Fail to reject null hypothesis

15)

There is insufficient evidence to support the claim that  New Yorkers watch more TV than theaverage American. In the population, Americans watch an average of 34 hours of TV per week.

16)

Effect Size = | µ sample - µ populaiton | / S = | 32 - 34 | / 5 = 0.4

17)

Effect is small.