Question

The following dette has become there toodetion of a storhen they wonderward in the art oy of Best Actress, along with the ages of actors whon they won in the category of Best Actor 26 Actress year) 25 25 31 Actor years) 58 40 37 38 23 25 30 30 34 26 3053 Use the sample data with a 0.01 significance level to beat the claim that for the population of age of Best Actresses and Best Actors, the differences have a mean loss than 0 (indicating that the Best Actresses we generally younger than Best Actors). In this example, is the mean value of the differences for the population of all pairs of data, where each individual difference is defined as the actress's age minus the actor's age. What are the nell and alternative hypotheses for the hypothesis test? How year(s) H₂:14 years) Type Integers or decimals. Do not round) Identify the best statistic (Round to two decimal places as needed.) Identify the value P value (Round to free decimal places as needed) What is the conclusion based on the hypothesis test? Since the values the significance level the nul hypothesis. There suficient evidence to support the claim that adresses we generally younger when they won the award the actors . Construct the confidence interval that could be used for the hypothesis of bed in part(). What feature of the confidence interval leads to the same conclusion reached in part?

Answer 1

Xi = the actress age (in years.) out actor age (in years) x the the dizi ixi-Yil differenie in agesi eld differences d for the The mean value of population of all pairs of data Here, n=10 di -35 -15 -80-14 12 -5 -38 -2 10 9 Edi= -120 Edi² = 3344 Idi = -120 = -12. - 2 s² = {di² nd? 3344-10(-12) n-1 9 ss 211.5555 s= 14:54 49 claim: The population of ages of Best Actresses and Best Actors the differences have a mean less than oi The null and alternative hypothers are, Hoë eld =0 years) Hp : eld po yearts) Test statistic, ed t = Ntni, Under Ho. stro CS

tal= -12 14.5449 / dto tral 2.63 ilt=-2061 p-value = P( t < -2.61) Plty 2.61) Ip-value = 0.014 (t-duta is symmetric) # p-value approach for testing we reject Mo at 2% level of significance if, p-value ad (1.0.5) giren that, significance level (d): 0.04(1.60) Here, p-value > 0.01 i e 0.014 70.ol we fail to reject Ho at + % level of significance Coocusion: since, the p-value is greater than the significance level, fail to reject, the null hypothesis . There is no f/ sufficient evidence to support the claim that actresses won the award generally younger then they than actors: are cs

b Here, we have to construct a gg% -ot for eld. significance level (2] = 0.01 (1%). We know that, a too (+2) % ol for eld is. (d; ta in-islo Here, tain-t = tool, g = 2.8214 Required as + (-12 2.8214. x 14.5499/10) (-24,97919 0.9711) ( - 25.0, 1.0 le . The CI is .-25.0/yearls) celd < (10 yeares) conclusion :- since, the reject the confidence interual contains zero fail to null hypothesis CSS CS