Question

Do the Academy Awards involve discrimination based on age?

Listed below are the ages of actresses and actors at the times that they won Oscars in the Best Actress and Best Actor categories. the ages are listed in order, beginning with the first Academy Awards ceremony in 1928. (Note: in 1968 there was a tie in the Best Actress category, and the mean of the two ages is used; in 1932 there was a tie in the Best Actor category, and the mean of the two ages is used)

BEST ACTRESSES

22	37	28	63	32	26	31	27	27	28
30	26	29	24	38	25	29	41	30	35
35	33	29	38	54	24	25	46	41	28
40	39	29	27	31	38	29	25	35	60
43	35	34	34	27	37	42	41	36	32
41	33	31	74	33	50	38	61	21	41
26	80	42	29	33	35	45	49	39	34
26	25	33	35	35	28	30	29	61

BEST ACTORS

44	41	62	52	41	34	34	52	41	37
38	34	32	40	43	56	41	39	49	57
41	38	42	52	51	35	30	39	41	44
49	35	47	31	47	37	57	42	45	42
44	62	43	42	48	49	56	38	60	30
40	42	36	76	39	53	45	36	62	43
51	32	42	54	52	37	38	32	45	60
46	40	36	47	29	43	37	38	45

QUESTIONS TO ANSWER:

1. Are there differences between the ages of the Best Actresses and the ages of the Best Actors?

2. Does it appear that actresses and actors are judged strictly on the basis of their artistic abilities?

3. Does thee appear to be discrimination based on age, with the Best Actresses tending to be younger than the Best Actors?

4. Are there any other notable differences?

* PROVIDE A GRAPH TO SHOW DATA (PIE, HISTO, ETC)*

*SUMMARY PARAGRAPH FOR RESULTS*

Answer 1

> Actors<-c(22,37,28,63,32,26,31,27,27,28,30,26,29,24,38,25,29,41,30,35,35,33,29,38,54,24,25,46,41,28,40,39,29,27,31,38,29,25,35,60,43,35,34,34,27,37,42,41,36,32,41,33,31,74,33,50,38,61,21,41,26,80,42,29,33,35,45,49,39,34,26,25,33,35,35,28,30,29,61)
> Actresses<-c(44,41,62,52,41,34,34,52,41,37,38,34,32,40,43,56,41,39,49,57, 41,38,42,52,51,35,30,39,41,44, 49,35,47,31,47,37,57,42,45,42,44,62,43,42,48,49,56,38,60,30,40,42,36,76,39,53,45,36,62,43,51,32,42,54,52,37,38,32,45,60,46,40,36,47,29,43,37,38,45)
> mean(Actors)
[1] 35.8481
> mean(Actresses)
[1] 43.79747
> sd(Actors)
[1] 11.26384
> sd(Actresses)
[1] 8.947682
> length(Actors)
[1] 79
> length(Actresses)
[1] 79

The provided sample means are shown below X1 35.8481 X43.79747 Also, the provided sample standard deviations are 1 11.26384 2 8.947682 and the sample sizes are n 79 and n79 (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested на: 41 # 2

This corresponds to a two-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used. Based on the information provided, the significance level is a 0.05, and the degrees of freedom are df 156. In fact, the degrees of freedom are computed as follows, assuming that the population variances are equal Hence, it is found that the critical value for this two-tailed test is t1.975, for a0.05 and df - 156 The rejection region for this two-tailed test is R {t: It > 1.975} Since it is assumed that the population variances are equal, the t-statistic is computed as follows: mi+n-2 n1 12 35.8481 - 43.79747 (79-1)11.263842 (79-1)8.9476822 11 -4.912 (4)_Decision about the null hypothesis Since it is observed thatt rejected. 4.912 te 1.975, it is then concluded that the null hypothesis is

Using the P-value approach: The p-value is p = 0, and since p 0 < 0.05, it is concluded that the null hypothesis is rejected. (5) Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population mean μι is different than μ , at the 0.05 significance level

We conclude that there are differences between the ages of the Best Actresses and the ages of the Best Actors.

Histogram of Actors CN 12 20 30 40 50 60 70 80 Actors

Histogram of Actresses 30 40 50 60 7080 Actresses

The graph shows average actors age is lower that actresses and so are median.