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) 25 25 33 26 32 26 26 45 28 35 Actor (years) 66 41 40 41 30 33 53 40 34 39 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, μd 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? H0: μd ________ ( A. =, B. ≠, C. <, D. > ) _______ year(s) H1: μd _______ ( A. =, B. ≠, C. <, D. > ) ________ 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 ____________( A. less than or equal to, B. greater than ) the significance level, __________( A. Fail to reject, B. Reject ) the null hypothesis. There ___________ ( A. is not, B. is ) 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) < μd < ____________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 ___________ ( A. zero, B. only negative numbers, C. only positive numbers ) , _____________( A. Fail to reject, B. Reject ) the null hypothesis.

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) 25 25 33 26 32 26 26 45 28 35 Actor (years) 66 41 40 41 30 33 53 40 34 39 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, μd 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? H0: μd ____ ( A. =, B. ≠, C. <, D. > ) _ year(s) H1: μd _ ( A. =, B. ≠, C. <, D. > ) 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 ( A. less than or equal to, B. greater than ) the significance level, ( A. Fail to reject, B. Reject ) the null hypothesis. There _ ( A. is not, B. is ) 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) < μd < __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 _ ( A. zero, B. only negative numbers, C. only positive numbers ) , _________( A. Fail to reject, B. Reject ) the null hypothesis.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 10CYU

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Section 9.3

Question #3

Actress (years)	25	25	33	26	32	26	26	45	28	35
Actor (years)	66	41	40	41	30	33	53	40	34	39

Actress (years)

Actor (years)

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, μ_dis 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?

H₀: μ_d________ ( A. =, B. ≠, C. <, D. > ) _______ year(s)

H₁: μ_d _______ ( A. =, B. ≠, C. <, D. > ) ________ 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 ____________( A. less than or equal to, B. greater than ) the significance level, __________( A. Fail to reject, B. Reject ) the null hypothesis. There ___________ ( A. is not, B. is ) 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) < μ_d < ____________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 ___________ ( A. zero, B. only negative numbers, C. only positive numbers ) , _____________( A. Fail to reject, B. Reject ) the null hypothesis.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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