The following data lists the ages of a random selection of actresses when they won an award in the category of Best Actress, along with the ages of actors when they won in the category of Best Actor. The ages are matched according to the year that the awards were presented. Complete parts (a) and (b) below. 26 29 32 37 24 28 42 Actress (years) 30 62 36 Actor (years) 40 34 32 34 52 35 27 32 D 38 42 Best Actresses are generally younger than Best Actors). In this example, p 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? но-на year(s) H₁: H<0 year(s) (Type integers or decimals. Do not round.) Identify the test statistic. t= -2.62 (Round to two decimal places as needed.) Identify the P-value. P-value = 0.014 (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? Since the P-value is greater than the significance level, fail to reject the null hypothesis. There is not sufficient evidence to support the claim that actresses are generally younger when they won the award than actors. b. Construct the confidence interval that could be used for the hypothesis test described in part (a). What feature of the confidence interval leads to the same conclusion reached in part (a)? The confidence interval is year(s)< < year(s). (Round to one decimal place as needed.)

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Answer part b only

The following data lists the ages of a random selection of actresses when they won an award in the category of Best Actress, along with the ages of actors when they won in the category of Best
Actor. The ages are matched according to the year that the awards were presented. Complete parts (a) and (b) below.
26
Actress (years) 30
Actor (years) 62 36
Best Actresses are generally younger than Best Actors).
In this example, Hd 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?
Ho: Hd =
42 27 32
29 32 37 24 28
40 34 32 34 52 35 38 42
0 year(s)
H₁: Ha
<0 year(s)
(Type integers or decimals. Do not round.)
Identify the test statistic.
t= -2.62 (Round to two decimal places as needed.)
Identify the P-value.
P-value = 0.014 (Round to three decimal places as needed.)
What is the conclusion based on the hypothesis test?
greater than
Since the P-value is
they won the award than actors.
b. Construct the confidence interval that could be used for the hypothesis test described in part (a). What feature of the confidence interval leads to the same conclusion reached in part (a)?
The confidence interval is year(s)<<
year(s).
(Round to one decimal place as needed.)
the significance level, fail to reject the null hypothesis. There is not sufficient evidence to support the claim that actresses are generally younger when
Transcribed Image Text:The following data lists the ages of a random selection of actresses when they won an award in the category of Best Actress, along with the ages of actors when they won in the category of Best Actor. The ages are matched according to the year that the awards were presented. Complete parts (a) and (b) below. 26 Actress (years) 30 Actor (years) 62 36 Best Actresses are generally younger than Best Actors). In this example, Hd 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? Ho: Hd = 42 27 32 29 32 37 24 28 40 34 32 34 52 35 38 42 0 year(s) H₁: Ha <0 year(s) (Type integers or decimals. Do not round.) Identify the test statistic. t= -2.62 (Round to two decimal places as needed.) Identify the P-value. P-value = 0.014 (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? greater than Since the P-value is they won the award than actors. b. Construct the confidence interval that could be used for the hypothesis test described in part (a). What feature of the confidence interval leads to the same conclusion reached in part (a)? The confidence interval is year(s)<< year(s). (Round to one decimal place as needed.) the significance level, fail to reject the null hypothesis. There is not sufficient evidence to support the claim that actresses are generally younger when
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