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) 27 29 28 28 35 25 27 41 29 33 Actor (years) 62 38 33 41 28 35 47 37 37 46. 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). H0:ud=0 H1:ud<0 Find the t value (test statistic) p value and 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).

Answer 1

Let's write null hypothesis (H0) and altermative hypothesis(H1)

Let's use minitab:

Step 1) First enter the given data set in minitab columns.

Step 2) Click on Stat >>>Basic statistics>>>Paired t

See the following image:

Then click on Option :

Look the following image:

Then click on OK again click on OK

So we get the following output:

From the above output we have

t = -2.73

p -value = 0.012

Decision rule:

1) If p-value < level of significance (alpha) then we reject null hypothesis

2) If p-value > level of significance (alpha) then we fail to reject null hypothesis.

Here p value = 0.012 < 0.05 so we used first rule.

That is we reject null hypothesis

Conclusion: At 5% level of significance there are sufficient evidence to say that for the population of ages of Best Actresses and Best Actors, the differences have a mean less than 0.

Here alternative hypothesis is is less than type, so the confidence interval is either one sided or need to obtained 90% confidence interval.

From the above output the upper bound of the 95% confidence interval of the differences is -3.35

Since the upper bound is less than zero, so we conclude that at 95% confidence that the population of ages of Best Actresses and Best Actors, the differences have a mean less than 0.