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Mental Health Classification

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Solution Summary

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 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
my mind 3 21 21 45
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.

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?