The following data lists the ages of a random selection of actresses when they won an award in the category of Best Actress, along with the ages of actors when they won in the category of Best Actor. The ages are matched according to the year that the awards were presented. Complete parts (a) and (b) below.Actress left parenthesis years right parenthesis25252827322525432836Actor left parenthesis years right parenthesis65353834293755424044a. Use the sample data with a 0.05 significance level to test the claim that for the population of ages of Best Actresses and Best Actors, the differences have a mean less than 0 (indicating that the Best Actresses are generally younger than Best Actors).

The paired t - test checks the mean difference between matched (or) paired data. The t- test statistic formula of paired t test defined by t=xdsdn~(n-1)df Where x̄ d is the mean of difference b/w two paired groups Sd is the standard deviation of the difference n is the sample sizeState Claim : The population mean difference for ages of Best Actresses and Best Actors is less than zero(0) State hypotheses : Null hypothesis H0: μd = 0 ; Population mean difference for ages of Best Actresses and Best Actors is 0 Alternative hypothesis H1: μd < 0; Population mean difference for ages of Best Actresses and Best Actors is less than 0 Compute the t -test statistic : d = difference between two groups ages Actress (xi) Actor (yi) di = xi-yi 25 65 -40 25 35 -10 28 38 -10 27 34 -7 32 29 3 25 37 -12 25 55 -30 43 42 1 28 40 -12 36 44 -8 ∑di =-125 We have values, ∑di =-125 & n = 10 Find the value of x̄d xd=∑din =-12510 =-12.5 then, Find the value of Sd sd=∑di-xd2n-1 =1548.510-1 =13.117 Substitute the values x̄d = -12.5, Sd = 13.117 & n = 10 in the above defined t - formula t=-12.513.11710=-12.513.117/3.1623=-12.54.148=-3.014 Therefore, the value of t - test statistic is -3.014 Calculation of p value: if t test statistic is -3.014 with n-1= 9 degrees of freedom then p value is 0.0073 [ use t- distribution table values] Therefore, the p value for the test is 0.0073 Rejection rule : if p value < significance level then null hypothesis Ho should be rejected. If not then null hypothesis Ho should not be rejected. Given significance level is 0.05 Conclusion : Thus, the obtained p value (0.0073) < 0.05. So, null hypothesis Ho should be rejected at 0.05significance level. Hence, it is concluding that the population of ages of Best Actresses and Best Actors, the differences have a mean less than 0.

Answered: The following data lists the ages of a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The following data lists the ages of a random selection of actresses when they won an award in the category of Best Actress, along with the ages of actors when they won in the category of Best Actor. The ages are matched according to the year that the awards were presented. Complete parts (a) and (b) below.
Actress left parenthesis years right parenthesis
25

Actor left parenthesis years right parenthesis
65

35
38
34
29
37
55
42
40
44
a. Use the sample data with a 0.05 significance level to test the claim that for the population of ages of Best Actresses and Best Actors, the differences have a mean less than 0 (indicating that the Best Actresses are generally younger than Best Actors).

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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