Listed below are ages of actresses and actors at the time that they won an award

Question

Listed below are ages of actresses and actors at the time that they won an award for the categories of Best Actress and Best Actor. Use the sample data to test for a difference between the ages of actresses and actors when they win the award. Use a 0.10 significance level. Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal. Actress's age 16 33 22 58 28 Actor's age 49 48 61 54 44 t = (Round to two decimal places as needed.) Identify the P-value. P-value = (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? Since the P-value is than the significant level, the null hypothesis. There sufficient evidence to support the claim that there is a difference between the ages of actresses and actors when they win the award.

Explanation / Answer

From information given,

difference (d)=Actress's age-Actor's age are as follows: -33, -15, -39, 4, -16. Use the formula for sample mean, xbar=sigma x/n and sample standard deviation, s=sqrt[1/n-1 sigma (x-xbar)^2] to compute dbar and sd respectively.

dbar=-19.80, sd=16.93

t=(dbar-0)/(sd/sqrt n)=(-19.80-0)/(16.93/sqrt 5)=-2.61

P value at 4 degrees of freedom [df=n-1, where n is number of pairs] is 0.059.

Less (0.059<0.10), Reject null hypothesis, There is sufficient evidence.

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