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Answer :
Final answer:
The null hypothesis (H₀) for the test is μₖ = 0, meaning on average there is no age difference between Best Actresses and Best Actors, while the alternative hypothesis (Hᴏ) is μₖ < 0, suggesting that Best Actresses are, on average, younger than Best Actors.
Explanation:
To test the claim that the population of ages of Best Actresses is generally younger than Best Actors, we can set up the following null and alternative hypotheses:
- The null hypothesis (H₀): μₖ = 0, which states that there is no difference in the mean age between Best Actresses and Best Actors.
- The alternative hypothesis (Hᴏ): μₖ < 0, which suggests that the mean age of Best Actresses is less than that of Best Actors, indicating that on average, Best Actresses are younger when they win the award.
To conduct this hypothesis test at a 0.05 significance level, we calculate the differences (actress's age - actor's age) for each paired set of data and examine whether the mean difference is significantly less than 0 using the appropriate statistical methods (such as a t-test, if assumptions are met).
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Final answer:
The null hypothesis (H0) is that there is no difference in mean age (mu Subscript d) between Best Actresses and Best Actors, represented as H0: mu Subscript d = 0. The alternative hypothesis (Ha) claims that actresses are younger on average, represented as Ha: mu Subscript d < 0. A t-test at the 0.05 significance level is used to test these hypotheses.
Explanation:
To test the claim that the population of ages of Best Actresses and Best Actors have a mean difference of ages less than 0, we need to set up null and alternative hypotheses for a hypothesis test. The null hypothesis (H0) will claim that there is no difference in the mean age (mu Subscript d) between actresses and actors, which is mathematically represented as H0: mu Subscript d = 0. The alternative hypothesis (Ha) claims that the mean age of actresses is less than that of actors, which is represented as Ha: mu Subscript d < 0.
To conduct the hypothesis test, we compare the actual mean differences we calculate from the sample with the null hypothesis using a t-test at a 0.05 significance level. If our test statistic falls within the critical region, we will reject the null hypothesis in favor of the alternative hypothesis, suggesting that actresses, on average, are younger than actors when they win the awards.
