Question

only 2 questions

((PLSS with steps and clear hand written PLSSS and thank you sooooo much for helping me))

Depression	Geographic location	Gender
3	Florida	Female
7	Florida	Male
7	Florida	Female
3	Florida	Female
8	Florida	Female
8	Florida	Male
8	Florida	Male
5	Florida	Female
5	Florida	Male
2	Florida	Female
6	Florida	Female
2	Florida	Female
6	Florida	Female
6	Florida	Male
9	Florida	Female
7	Florida	Male
5	Florida	Male
4	Florida	Male
7	Florida	Female
3	Florida	Female
8	New York	Female
11	New York	Male
9	New York	Male
7	New York	Male
8	New York	Female
7	New York	Male
8	New York	Female
4	New York	Male
13	New York	Female
10	New York	Male
6	New York	Female
8	New York	Female
12	New York	Female
8	New York	Male
6	New York	Male
8	New York	Male
5	New York	Male
7	New York	Female
7	New York	Male
8	New York	Male
10	North Carolina	Male
7	North Carolina	Female
3	North Carolina	Male
5	North Carolina	Male
11	North Carolina	Female
8	North Carolina	Female
4	North Carolina	Male
3	North Carolina	Male
7	North Carolina	Female
8	North Carolina	Male
8	North Carolina	Female
7	North Carolina	Female
3	North Carolina	Female
9	North Carolina	Female
8	North Carolina	Female
12	North Carolina	Female
6	North Carolina	Male
3	North Carolina	Male
8	North Carolina	Male
11	North Carolina	Female

As part of a long-term study of individuals 65 years of age or older, sociologists and physicians at the Wentworth Medical Center in upstate New York investigated the relationship between geographic location, gender and depression. A sample of 60 individuals, all in reasonably good health, was selected; 20 individuals were residents of Florida, 20 were residents of New York, and 20 were residents of North Carolina. Each of the individuals sampled was given a standardized test to measure depression. The data collected follow; higher test scores indicate higher levels of depression.

........

h) Is there any significant difference of the mean of depression value due to geographic location? Use a 0.05 level of significance.

i) Give point estimates for the proportion of individuals according to their gender.

Answer 1

h) Based on the given data, our objective is to compare the depression levels of people across three different geographical areas . Let denote the mean depression levels of people from - Florida, New York and North Carolina respectively.

To test: Vs H_a: Not all means are equal

The appropriate test here, would be One way ANOVA. To run the test, using excel, we must first arrange the data in the following manner:

The output obtained is:

Since the p-value of the test 0.008 < 0.05, we find that the test result is significant. We do not have sufficient evidence to support the null hypothesis. We may reject H₀ at 5% level of significance.

We may conclude that not all three means are equal i.e, there is a significant difference of the mean of depression value due to geographic location.

i) Using excel,

Estimated proportion of females = No. of females in the given sample / Total no. of individuals in the given sample

= 31 / 60

=

Similarly,

Estimated proportion of males = No. of males in the given sample / Total no. of individuals in the given sample

= 29 / 60

=