The following data lists the ages of a random selection of actresses when they won an award in the category 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) 30 Actor (years) 68 27 29 39 34 29 41 ▼ 37 28 Ho Pa year(s) H₁ Hd year(s) (Type integers or decimals. Do not round.) 27 25 43 32 36 56 39 34 ***** ages of Best Actresses a. Use the sample data with a 0.05 significance level to test the claim that for the population and Best Actors, the differences have a mean less than 0 (indicating that the Best Actresses are generally younger than Best Actors). 35 39 In this example, 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?
The following data lists the ages of a random selection of actresses when they won an award in the category 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) 30 Actor (years) 68 27 29 39 34 29 41 ▼ 37 28 Ho Pa year(s) H₁ Hd year(s) (Type integers or decimals. Do not round.) 27 25 43 32 36 56 39 34 ***** ages of Best Actresses a. Use the sample data with a 0.05 significance level to test the claim that for the population and Best Actors, the differences have a mean less than 0 (indicating that the Best Actresses are generally younger than Best Actors). 35 39 In this example, 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?
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Transcribed Image Text:### Data Analysis of Best Actress and Best Actor Award Winners
The following data presents the ages of a random selection of actresses when they won an award for Best Actress, along with the ages of actors when they won for Best Actor. The ages are matched according to the year the awards were presented.
| Awards Category | Ages (years) |
|-----------------|--------------------------|
| Actress | 30, 27, 29, 29, 37, 27, 25, 43, 32, 35 |
| Actor | 68, 34, 39, 41, 28, 36, 56, 39, 34, 39 |
#### Hypothesis Testing
**Objective:** Use the sample data with a 0.05 significance level to test the claim that the mean age differences between Best Actresses and Best Actors is less than 0. This would indicate that Best Actresses are generally younger than Best Actors.
- **Mean of Differences (μ<sub>d</sub>):** This is calculated based on the actress's age minus the actor's age for each pair of winners.
**Formulate the Hypotheses:**
- **Null Hypothesis (H<sub>0</sub>):** μ<sub>d</sub> ≥ 0 year(s)
- **Alternative Hypothesis (H<sub>1</sub>):** μ<sub>d</sub> < 0 year(s)
**Note:** Please input the integer or decimal value for μ<sub>d</sub>; do not round the number.
This test will help determine if there is a statistically significant difference in the ages of male and female award winners in these categories, suggesting potential age-related trends in the film industry.
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