Question

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method.

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 33 29 27 27 37 41 28 38 26 21 33 42 32 30 35

Best Actors 30 41 48 52 40 39 62 34 34 62 42 56 41 33 29

Answer 1

= (3 + (-12) + (-21) + (-25) + (-3) + 2 + (-34) + 4 + (-8) + (-41) + (-9) + (-14) + (-9) + (-3) + 6)/15 = -10.93

s_d = sqrt(((3 + 10.93)^2 + (-12 + 10.93)^2 + (-21 + 10.93)^2 + (-25 + 10.93)^2 + (-3 + 10.93)^2 + (2 + 10.93)^2 + (-34 + 10.93)^2 + (4 + 10.93)^2 + (-8 + 10.93)^2 + (-41 + 10.93)^2 + (-9 + 10.93)^2 + (-14 + 10.93)^2 + (-9 + 10.93)^2 + (-3 + 10.93)^2 + (6 + 10.93)^2)/14) = 10.038

The test statistic is

  

df = 15 - 1 = 14

P-value = P(T < -4.217)

= 0.0004

Since the P-value is less than the significance level (0.0004 < 0.01), so we should reject the null hypothesis.

At 0.01 significance level, there is sufficient evidence to support the claim that best actresses are younger than best actors.