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# Chi square test of independence and ANOVA

See attached file for full problem description.

1. A teacher figures that final grades in the statistics department are distributed as A-25%, B-25%, C-40%, D-5%, and F-5%. At the end of a randomly selected semester, the following number of grades were recorded. Determine if the grade distribution for the department is different than expected. Use &#61537; = 0.01.

Grade A B C D F
Number 42 36 60 14 8

2. The contingency table below shows the results of a random sample of 200 state representatives that was conducted to see whether their opinions on a bill are related to party affiliation.

Party Approve Disapprove No Opinion
Republican 42 20 14
Democrat 50 24 18
Independent 10 16 6

3. Find the critical value of F to test the claim that . Two samples are randomly selected form populations that are normal. The sample statistics are given below. Use &#61537; = 0.05.

= 16, s = 8.41; = 15, s = 7.84

4. At a college, 61 female students were randomly selected and it was found that their monthly income had a standard deviation of \$133.65. For 121 male students the standard deviation was \$185.57. Test the claim that the variance of monthly incomes is higher for male students that it is for female students. Use &#61537; = 0.05

5. Four different types of fertilizers are used on raspberry plants. The number of raspberries on each randomly selected plant is given below. Find the test statistic F to test the claim that the type of fertilizer makes no difference in the mean number of raspberries. Use &#61537; = .05

Fertilizer 1 Fertilizer 2 Fertilizer 3 Fertilizer 4
6 5 6 3
7 8 3 5
5 5 4 3
6 5 2 4
7 5 3 4
6 6 3 5

#### Solution Summary

The solution gives detailed steps of ANOVA, Chi-square, and f test. Null hypothesis, alternative hypothesis, critical Value, p value and test statistics are given with interpretation.

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