Listed below are the ages of actresses and actors at the times that they won Oscars for the categories of Best Actress and Best Actor. The ages are listed in chronological order by row, so that corresponding locations in the two tables are from the same year. (Notes: 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 are used. These Data are suggested by the article “Ages of Oscar-winning Best Actors and Actresses” by Richard Brown and Gretchen Davis. Mathematics Teacher magazine. In that article, the year of birth of the award winner was subtracted from the year of the awards ceremony but the ages in the tables below are based on the birth date of the winner and the date of the awards ceremony.)
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
46
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
a) First explore the data using suitable statistics and graphs. Use the results to make informal comparisons.
b) Determine whether there are significant differences between the ages of the Best Actresses and the ages of the Best Actors. Use appropriate hypothesis tests. Describe the methods used and the conclusions reached.
c) Discuss cultural implications of the results. Does it appear that actresses and actors are judged strictly on the basis of their artistic abilities? Or does there appear to be discrimination based on age, with the Best Actresses tending to be younger that the Best Actors? Are there any other notable differences?
Find the means first = sum of scores/number of scores
Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.
Standard deviation = square root of variance
Z = (mean1 - mean2)/standard error (SE) of difference between means
SEdiff = √(SEmean1^2 + SEmean2^2)
SEm = SD/√n
If only one SD is provided, you can use just that to determine SEdiff.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.
I'll let you do the calculations and come to your own conclusions.
To explore the data and make informal comparisons, we can analyze the ages of the Best Actresses and Best Actors using suitable statistics and graphs. Let's start by calculating some basic statistics.
a) Statistics:
- Mean (average): Calculate the mean age for both Best Actresses and Best Actors.
- Median: Calculate the median age for both Best Actresses and Best Actors.
- Range: Find the range (maximum age minus minimum age) for both Best Actresses and Best Actors.
- Standard Deviation: Calculate the standard deviation for the ages of both Best Actresses and Best Actors. This will give an indication of the spread of data around the mean.
b) Hypothesis Test:
To determine whether there are significant differences between the ages of the Best Actresses and Best Actors, we can perform a hypothesis test. We will use a two-sample t-test to compare the means of the two groups.
Null hypothesis (H0): There is no significant difference in the mean ages of Best Actresses and Best Actors.
Alternative hypothesis (Ha): There is a significant difference in the mean ages of Best Actresses and Best Actors.
To perform the t-test, we will assume that the data are normally distributed and that the variances of the two groups are equal. If the p-value is less than the significance level (commonly 0.05), we reject the null hypothesis and conclude that there is a significant difference in the mean ages of Best Actresses and Best Actors.
c) Cultural Implications:
To discuss the cultural implications of the results, we can analyze the findings from the statistical analysis. If there is a significant difference in the mean ages of Best Actresses and Best Actors, it raises questions about potential discrimination based on age. Additionally, if one group tends to be consistently younger than the other, it suggests that there may be biases towards younger actors/actresses in the Oscar voting process.
It is important to note that these implications are based on statistical analysis and overall trends. They may not explain the individual circumstances of each award winner, as there can be various factors influencing the selection process in any given year.
Now let's perform the necessary calculations and hypothesis test to further explore the data.