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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. Actress (years) 27 30 32 32 Actor (years) 58 41 35 38 39 29 23 37 27 36D 27 34 49 38 35 38 a. Use the sample data with a 0.05 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, 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: Ha 0 year(s) H₁ Hd< 0 year(s) (Type integers or decimals. Do not round.) Identify the test statistic. t= -2.06 (Round to two decimal places as needed.) Identify the P-value. P-value = 0.035 (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, they won the award than actors. reject the null hypothesis. There is sufficient evidence to support the claim that actresses are generally younger when 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)

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. Actress (years) 27 30 32 32 Actor (years) 58 41 35 38 39 29 23 37 27 36D 27 34 49 38 35 38 a. Use the sample data with a 0.05 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, 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: Ha 0 year(s) H₁ Hd< 0 year(s) (Type integers or decimals. Do not round.) Identify the test statistic. t= -2.06 (Round to two decimal places as needed.) Identify the P-value. P-value = 0.035 (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, they won the award than actors. reject the null hypothesis. There is sufficient evidence to support the claim that actresses are generally younger when 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)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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. Actress (years) 27 30 32 32 Actor (years) 58 41 35 38 39 29 23 37 27 36D 27 34 49 38 35 38 a. Use the sample data with a 0.05 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, 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: Ha 0 year(s) H₁ Hd< 0 year(s) (Type integers or decimals. Do not round.) Identify the test statistic. t= -2.06 (Round to two decimal places as needed.) Identify the P-value. P-value = 0.035 (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, they won the award than actors. reject the null hypothesis. There is sufficient evidence to support the claim that actresses are generally younger when 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) <Hd ☐ year(s). (Round to one decimal place as needed.)
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. Actress (years) 27 30 32 32 Actor (years) 58 41 35 38 39 29 23 37 27 36D 27 34 49 38 35 38 a. Use the sample data with a 0.05 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, 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: Ha 0 year(s) H₁ Hd< 0 year(s) (Type integers or decimals. Do not round.) Identify the test statistic. t= -2.06 (Round to two decimal places as needed.) Identify the P-value. P-value = 0.035 (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, they won the award than actors. reject the null hypothesis. There is sufficient evidence to support the claim that actresses are generally younger when 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) <Hd ☐ year(s). (Round to one decimal place as needed.)
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