The following data lists the ages of a random selection ofactresses when they won an award in the category of Best? Actress,along with the ages of actors when they won in the category of BestActor. The ages are matched according to the year that the awardswere presented. Complete parts? (a) and? (b) below.
a. Use the sample data with a
0.010.01
significance level to test the claim that for the population ofages of Best Actresses and Best? Actors, the differences have amean less than 0? (indicating that the Best Actresses are generallyyounger than Best?Actors).In this? example,
mu Subscript d?d
is the mean value of the differences d for the population of allpairs of? data, where each individual difference d is defined asthe? actress's age minus the? actor's age. What are the null andalternative hypotheses for the hypothesis? test?
Upper H 0H0?:
mu Subscript d?d
equals=
00 ?year(s)
Upper H 1H1?:
mu Subscript d?d
less than<
00 ?year(s)
?(Type integers or decimals. Do not? round.)
Identify the test statistic.
tequals=negative 3.68?3.68
?(Round to two decimal places as? needed.)
Identify the? P-value.
?P-valueequals=0.0020.002
?(Round to three decimal places as? needed.)
What is the conclusion based on the hypothesis? test?
Since the? P-value is
less than or equal to
the significance? level,
reject
the null hypothesis. There
is
sufficient evidence to support the claim that actresses aregenerally younger when they won the award than actors.
b. Construct the confidence interval that could be used for thehypothesis test described in part? (a). What feature of theconfidence interval leads to the same conclusion reached in part?(a)?
The confidence interval is
nothing
?year(s)less than?year(s).
?(Round to one decimal place as? needed.)
What feature of the confidence interval leads to the sameconclusion reached in part? (a)?
Since the confidence interval contains
zero,
only positive numbers,
only negative numbers,
reject
fail to reject
the null hypothesis.
Actress (years) Actor (years)
30 58
30 41
31 35
28 42
33 31
27 34
25 46
42 38
29 41
31 43
