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 yearthat the awards were presented. Complete parts (a) and (b) below.30Actress (years) 29Actor (years)263232262839323567333534283655394140a. Use the sample data with a 0.01 significance level to test the claim that for the population of ages of Best Actresses and Best Actors, the differences have a mean less than 0 (indicating that the Best Actresses are generally younger than BestActors).In this example, µa 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 thehypothesis test?Ho: Hdyear(s)H1: Hdyear(s)(Type integers or decimals. Do not round.)Identify the test statistic.t =(Round to two decimal places as needed.)Identify the P-value.P-value =(Round to three decimal places as needed.)What is the conclusion based on the hypothesis test?Since the P-value isthe significance level,the null hypothesis. Theresufficient 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)< Hyear(s).(Round to one decimal place as needed.)What feature of the confidence interval leads to the same conclusion reached in part (a)?Since the confidence interval containsthe null hypothesis.

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Description: 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 yearthat th

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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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.
30
Actress (years) 29
Actor (years)
26
32
32
26
28
39
32
35
67
33
35
34
28
36
55
39
41
40
a. Use the sample data with a 0.01 significance level to test the claim that for the population of ages of Best Actresses and Best Actors, the differences have a mean less than 0 (indicating that the Best Actresses are generally younger than Best
Actors).
In this example, µa 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
year(s)
H1: Hd
year(s)
(Type integers or decimals. Do not round.)
Identify the test statistic.
t =
(Round to two decimal places as needed.)
Identify the P-value.
P-value =
(Round to three decimal places as needed.)
What is the conclusion based on the hypothesis test?
Since the P-value is
the significance level,
the null hypothesis. There
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)< H
year(s).
(Round to one decimal place as needed.)
What feature of the confidence interval leads to the same conclusion reached in part (a)?
Since the confidence interval contains
the null hypothesis.

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The given data for matches of ages of actors and actresses when the awards were presented are listed below:

Actress	Actor
29	67
26	33
30	35
32	34
32	28
26	36
28	55
39	39
32	41
35	40

It is required to test the claim that for the population of ages of Best Actress and Best Actors the difference has a mean less than 0.

The given level of significance is

α = 0.01

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