Question

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 )31 31 32 26 32 28 29 43 29 32 Actor (years )62 34 32 41 26 33 47 42 40 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, mu Subscript d 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?

Answer 1

Null Hypothesis
`\mu_(d)=0` years

Alternative hypothesis
`\mu_(d)<0` years

Explanation:

Hypothesis is a tentative guess. In a null hypothesis,
`H_(o)` we state that there's no statistical significance between the variables. For alternative hypothesis,
`H_(1)` it's stated that there's significant statistical relation between the provided variables. In this case, the null Hypothesis is
`\mu_(d)=0` years and the alternative hypothesis is
`\mu_(d)<0` years

We can decide to accept or reject either null hypothesis or alternative hypothesis