Question

Using your sample of actors, test the hypothesis that the average age of men at the time they won an Oscar for Best Performance in a Leading role is greater than 45. To receive full credit include: (Ho, Ha, p-value, reject or fail to reject and a conclusion in plain English)

Actor (Random Number Generator)	Age upon receiving award
Maximilian Schell	31
Marlon Brando	31
James Stewart	32
Eddie Redmayne	33
Charles Laughton	34
Fredric March	35
Russell Crowe	36
Charlton Heston	36
Jamie Foxx	37
Tom Hanks	37
Rami Malek	37
Sidney Poitier	37
Broderick Crawford	38
Tom Hanks	38
Philip Seymour Hoffman	38
Spencer Tracy	38
Jack Nicholson	38
Ray Milland	39
José Ferrer	39
Kevin Spacey	40
Warner Baxter	41
Jeremy Irons	42
Michael Douglas	43
Sean Penn	43
George C. Scott	43
F. Murray Abraham	45
Paul Scofield	45
Joaquin Phoenix	45
Geoffrey Rush	45
Forest Whitaker	45
Gregory Peck	47
Paul Lukas	48
Victor McLaglen	49
Daniel Day-Lewis	50
Humphrey Bogart	52
Robert Duvall	53
Ronald Colman	57
John Wayne	62
Paul Newman	62
Henry Fonda	76

Answer 1

Ho: =45 and Ha: <45, where is the average of actors when they won Oscars for best performance while leading.

We will be conducting a one-sample t-test to test the hypothesis. The test statistic is given by:

. The test statistic follows a t-distribution with 39 degrees of freedom. Thus the p-value is given by: . If we are testing at a significance level of 0.05. Then as the p-value is more than 0.05 thus we fail to reject the null hypothesis.

Conclusion: There is not sufficient evidence to support the claim that the average of actors when they won Oscars for best performance while leading is less than 45 years.