Question

Listed below are ages of actresses and actors at the time that they won an award for the categories of Best Actress and Best Actor. Use the sample data to test for a difference between the ages of actresses and actors when they win the award. Use a 0.05 significance level. Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal. ?Actress's age 20 26 20 49 26 ?Actor's age 43 42 63 52 42 In this? example, mu Subscript d is the mean value of the differences d for the population of all pairs of? data, where each individual difference d is defined as the? actress's age minus the? actor's age. What are the null and alternative hypotheses for the hypothesis? test? A. Upper H 0?: mu Subscript dnot equals0 Upper H 1?: mu Subscript dgreater than0 B. Upper H 0?: mu Subscript dnot equals0 Upper H 1?: mu Subscript dequals0 C. Upper H 0?: mu Subscript dequals0 Upper H 1?: mu Subscript dless than0 D. Upper H 0?: mu Subscript dequals0 Upper H 1?: mu Subscript dnot equals0 Identify the test statistic. tequals nothing ?(Round to two decimal places as? needed.) Identify the? P-value. ?P-valueequals nothing ?(Round to three decimal places as? needed.) What is the conclusion based on the hypothesis? test? Since the? P-value is ? less greater than the significance? level, ? reject fail to reject the null hypothesis. There ? is not is sufficient evidence to support the claim that there is a difference between the ages of actresses and actors when they win the award.

Answer 1

data

actress	actor
20	43
26	42
20	63
49	52
26	42

excel result

t-Test: Paired Two Sample for Means
	actress	actor
Mean	28.2	48.4
Variance	144.2	84.3
Observations	5	5
Pearson Correlation	0.062582466
Hypothesized Mean Difference	0
df	4
t Stat	-3.082622538
P(T<=t) one-tail	0.018418754
t Critical one-tail	2.131846786
P(T<=t) two-tail	0.036837508
t Critical two-tail	2.776445105

since p-value = 0.0368 < 0.05

we reject the null hypothesis

we conclude that there is sufficient evidence that there is a difference between the ages of actresses and actors when they win the award.