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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) 25 Actor (years) 27 28 28 37 26 25 44 27 33 59 35 35 39 29 37 55 35 37 39 ...... IUCI ILIY LI ICI vaIut. P-value = 0.023 (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test?

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 Actor (years) 27 28 28 37 26 25 44 27 33 59 35 35 39 29 37 55 35 37 39 ...... IUCI ILIY LI ICI vaIut. P-value = 0.023 (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test?

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) | 25 | 27 | 28 | 28 | 37 | 26 | 25 | 44 | 27 | 33 | | Actor (years) | 59 | 35 | 35 | 39 | 29 | 37 | 55 | 35 | 37 | 39 | P-value = 0.023 (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 \[ \_\_ \] years < μd < \[ \_\_ \] years. (Round to one decimal place as needed.) Get more help.
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) | 25 | 27 | 28 | 28 | 37 | 26 | 25 | 44 | 27 | 33 | | Actor (years) | 59 | 35 | 35 | 39 | 29 | 37 | 55 | 35 | 37 | 39 | P-value = 0.023 (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 \[ \_\_ \] years < μd < \[ \_\_ \] years. (Round to one decimal place as needed.) Get more help.
The image contains text and a table related to a statistical hypothesis test. Here's the transcription suitable for an educational website: --- ### Hypothesis Testing of Actor and Actress Ages The following data represents a selection of actresses and actors, along with their ages at the time they won in the category of Best Actor and Best Actress. The ages are paired according to the year in which they were awarded. The test compares the ages of actresses and actors as detailed below: | Actress (years) | 25 | 38 | 28 | 33 | 35 | 35 | 30 | |----------------|----|----|----|----|----|----|----| | Actor (years) | 45 | 29 | 32 | 35 | 55 | 37 | 39 | **Objective:** Using the sample data at a 0.01 significance level, test the claim that for the population of ages of Best Actresses and Best Actors, the differences have a mean less than 0. Concluding that the Best Actresses are generally younger. Define the test statistic `t` as the mean value of the differences of the ages for the population of all pairs of data, where each difference is defined as the actress's age minus the actor's age. **Hypotheses:** - \( \text{H}_0 \): \(\mu_d = 0\) (The mean difference is not less than 0) - \( \text{H}_1 \): \(\mu_d < 0\) (The mean difference is less than 0) 1. **Identify the test statistic:** - \( t = -2.714 \) (rounded to three decimal places) 2. **P-value:** - \( 0.032 \) (rounded to three decimal places) **Conclusion:** Since the p-value is 0.032, which is greater than the 0.01 significance level, we do not reject the null hypothesis. Therefore, there is not enough evidence to support the claim that Best Actresses are generally younger than Best Actors at the time they receive their awards. --- For further assistance: - **Help me solve this** - **View an example** - **Get more help**
Transcribed Image Text:The image contains text and a table related to a statistical hypothesis test. Here's the transcription suitable for an educational website: --- ### Hypothesis Testing of Actor and Actress Ages The following data represents a selection of actresses and actors, along with their ages at the time they won in the category of Best Actor and Best Actress. The ages are paired according to the year in which they were awarded. The test compares the ages of actresses and actors as detailed below: | Actress (years) | 25 | 38 | 28 | 33 | 35 | 35 | 30 | |----------------|----|----|----|----|----|----|----| | Actor (years) | 45 | 29 | 32 | 35 | 55 | 37 | 39 | **Objective:** Using the sample data at a 0.01 significance level, test the claim that for the population of ages of Best Actresses and Best Actors, the differences have a mean less than 0. Concluding that the Best Actresses are generally younger. Define the test statistic `t` as the mean value of the differences of the ages for the population of all pairs of data, where each difference is defined as the actress's age minus the actor's age. **Hypotheses:** - \( \text{H}_0 \): \(\mu_d = 0\) (The mean difference is not less than 0) - \( \text{H}_1 \): \(\mu_d < 0\) (The mean difference is less than 0) 1. **Identify the test statistic:** - \( t = -2.714 \) (rounded to three decimal places) 2. **P-value:** - \( 0.032 \) (rounded to three decimal places) **Conclusion:** Since the p-value is 0.032, which is greater than the 0.01 significance level, we do not reject the null hypothesis. Therefore, there is not enough evidence to support the claim that Best Actresses are generally younger than Best Actors at the time they receive their awards. --- For further assistance: - **Help me solve this** - **View an example** - **Get more help**
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