5. Every year at the Oscar the age of the winning best actress and best actor ar

Question

5. Every year at the Oscar the age of the winning best actress and best actor are recorded. On average, over the past 12 years, the best actress is 10.2 years younger than the best actor. The standard deviation of the differences in age is s 14.7. Test if the average age of the best actress winner is less than the average age of the winner for best actor. Assume that the difference in ages follows a Normal distribution. Use a) Write out the null and alternative hypotheses. b) What is the value of the test statistic? c) What is the p-value? d) What is the conclusion regarding Ho? e) Interpret your decision in the context of the problem.

Explanation / Answer

a)

b)

c)

d)as p value is less than 0.1 level we reject null hypothesis

e) we have evidence to conclude that mean age of best actress winner is less than mean age of best actor.

null Hypothesis: d = 0 alternate Hypothesis: d < 0 for 0.1 level with left tailed test and n-1= 11 degree of freedom, critical value of t= 1.3634 Decision rule :                   reject Ho if test statistic t<-1.363

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