Listed below are ages of actresses and actors from a country at the times that t

Question

Listed below are ages of actresses and actors from a country at the times that they won a certain award. The data are paired according to the years that they won. Use a 0.01 significance level to test the belief that best actresses are younger than best actors. Does the result suggest a problem in that culture? Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal Best Actresses 32 27 40 33 26 40 27 38 42 28 24 35 21 27 29 Best Actors 25 41 28 42 34 49 48 39 56 62 40 29 62 52 41 [ | a problem in that culture. [-dHo-There is Since the test statistic In the critical region, Ho. There is evidence to support the belief that best actresses are younger than best actors. This result appears to suggest that there

Explanation / Answer

The R code is:

actresses=c(32,27,40,33,26,40,27,38,42,28,24,35,21,27,29)
actors=c(25,41,28,42,34,49,48,39,56,62,40,29,62,52,41)
t.test(actresses,actors,paired = T)

The output is:

Paired t-test

data: actresses and actors

t = -3.1494, df = 14,

p-value = 0.0071

alternative hypothesis: true difference in means is not equal to 0

95 percent confidence interval:

-20.06002 -3.80665

sample estimates:

mean of the differences

-11.93333

Since the p-value is 0.0071, so the null hypothesis is rejected.

Since the test statistic fall in the critical region, reject H0. There is sufficient evidence to support that best actresses are younger than best actors. The results appear to suggest that there is a problem in that culture.

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