# Mental Health Classification

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1. A study was conducted that examined the relationship between mentah-health classification and thoughts of suicide. The mental health of each person in a sampl of 295 was classified as normal, mild psychiatric illness or severe psychiatric illness. Also, each person was asked: "Have you recently found that the idea of taking your own life kept coming into your mind?" Following are the results.

Mental Health

Normal Mild

Illness Severe

Illness Total

Response Definitely

not 90 43 34 167

Don't think

so 5 18 8 31

Crossed

my mind 3 21 21 45

Definitely

yes 1 15 36 52

Total 99 97 99 295

Is there evidence that response to the suicide question and mental-health classification are independent? Perform the required hypothesis test at the 0.05 level of significance?

2. A researcher decided to compare the theoretical distribution of M&M candy colors to a sample of three randomly selected bags of the candy. The theoretical distribution is

Color Percentage

Brown 30

Yellow 20

Red 20

Orange 10

Green 10

Blue 10

From the three bags of candy purchased from different stores, the distribution of the colors was

Color Frequency

Brown 152

Yellow 114

Red 106

Orange 51

Green 43

Blue 43

Does the data indicate that the color distribution of M&Ms is the same as the distribution claimed by the company? Use the 0.05 level of significance.

3. A poll was taken to determine the feelings of voters toward instituting regional (vice state) primary elections for presidential candidates. Voters were asked to state a party affiliation and express their opinion on regional primaries. The results are below.

Response

Good Idea Poor Idea No Opinion Total

Affiliation Rep 266 266 186 718

Dem 308 251 176 735

Ind 28 27 21 76

Total 602 544 383 1529

At the 0.05 level of significance, do the data suggest that the opinions of voters on the issue of regional primaries are associated with political affiliation

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##### Solution Summary

The significance levels for mental health classifications are provided. Political affiliation issues are determined.

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these are questions of CHI square test for independence and goodness of fitness.

1. A study was conducted that examined the relationship between mental-health classification and thoughts of suicide. The mental health of each person in a sample of 295 was classified as normal, mild psychiatric illness or severe psychiatric illness. Also, each person was asked: "Have you recently found that the idea of taking your own life kept coming into your mind?" Following are the results.

Mental Health

Normal Mild

Illness Severe

Illness Total

Response Definitely not 90 43 34 167

Don't think so 5 18 8 31

Crossed my mind 3 21 21 45

Definitely yes 1 15 36 52

Total 99 97 99 295

Is there evidence that response to the suicide question and mental-health classification are independent? Perform the required hypothesis test at the 0.05 level of significance?

Create a table of cell frequencies.

The first step in computing the chi square test of independence is to compute the expected frequency for each cell under the assumption that the null hypothesis is true. To calculate the expected frequency of the first cell in the example (experimental condition, graduated), first calculate the proportion of subjects that graduated without considering the condition they were in. The table shows that of the 295 subjects in the experiment, 99 have Normal Mental Health. Therefore, the proportion is 99/295. If the null hypothesis were true, the expected frequency for the first cell would equal the product of the number of people in the experimental ...

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