Question

Inferences from Two Samples chapter Listed below are the ages of actresses the awards ceremony, but the ages in and actors at the times that they won the table below are based on the birth Oscars for the categories of Best Actress date of the winner and the date of the and Best Actor. The ages aze listed in awards certmony) chronological otder by row, so that cor- responding locations in the two tables Analyzing the Results are from the same year. (Note: In 1968 1. First oplore the data using suitable there was a tie in the Best Actress cate statistics and graphs. Use the results to gory, and the mean of the two ages is make informal comparisons. 2. Determine whether there are signif cant differences between the ages of the actors are judged strictly on the basis of ther artistic abilities? Or does there ap- used; in 1932 there was ate inthe Best Actor category, and the mean of the two ages is used. These data are suggested by the article "Ages of Oscar-winning Best Actors and Actresses," by Richard Brown and Gretchen Davis, pear to be discrimination based on age, with the Best Actresses tending to be Best Actresses and the ages of the Best Actors. Use appropriate hypothesis tests.younger than the Best Actos? Aze there Describe the methods used and the con- any other notable differences Use clusions reached. Mathematia Tacher magazine. In that article, the year of birth of the award3. Discuss cultural implications of the winner was subtracted from the year of reruls. Does it appear that actresses and Best Actresses Best Actors 22 37 28 63 32 26 31 27 27 28 44 41 62 52 41 34 34 52 41 37 50 26 29 24 38 25 29 41 30 35 38 34 32 40 43 56 41 39 49 57 35 33 29 38 54 24 25 46 41 28 41 38 42 52 51 35 30 3941 4 40 39 29 27 31 38 29 25 35 60 49 35 47 31 47 37 57 42 45 42 43 35 34 34 27 37 42 41 36 32 62 43 42 48 49 56 38 60 30 41 33 31 74 33 50 38 61 21 41 40 42 36 76 39 53 45 36 62 26 80 42 29 33 35 45 49 39 34 51 52 42. 54 52 37 3 32 o 46 40 36 47 29 43 7 38 45 26 25 33 35 35 28 30 29 61 MacBook Pro

Answer 1

1) The scatter plot shown below shows that the mean age of best actresses seems lower than that of best actors. Additionally, the variance of the ages of such actresses are higher than those of such actors, as can also be seen from the table shown below:

Age of actresses/actors 70 501 . 40 20 Tii Tii 20 40 50 70 80 Best Actresses Best Actors

	Best Actresses	Best Actors
Mean	35.72	43.54
Std Dev	11.30	8.94

2) Let's use the 2-sided t-test for comparing the population means of best actresses and best actors:

Hypotheses:

H₀: $\mu_1 - \mu_2 = 0$

H_a: $\mu_1 - \mu_2 \ne 0$

Test statistic, t-stat = ($\bar{x_1} - \bar{x_2}$) / sqrt[(s_g^2/n_g) + (s_b^2/n_b)], where $\bar{x_g}$ and $\bar{x_b}$ are the sample means, s_g and s_bare the sample variances, and n_g and n_b are the sample sizes of grooms and brides respectively.

= - 4.824 (using values from table obtained in part 1, and sample size = 79 each)

Assuming a significance level of 5%, critical t-score for the 2-tailed test, t_{0.975, 77} = 1.990

So, |t-statistic| > t_{0.975, 77} => we can reject the null hypothesis that the means of the ages are equal at a significance level of 5%.

Hence, the populations means are indeed significantly different.

3) From the results above, it does look like there is a bias towards rewarding younger actresses being awarded with more probability. So, artistic abilities might not be the only factor for rewarding the actresses.

Another notable difference is that the variance/spread in the ages of best actresses is higher compared to that of best actors.