Expert answer:Hypothesis and P-value

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18.
A MiniMart sells five different types of teddy bears. The manager reports that the five types are
equally popular. Suppose that a sample of 500 purchases yields observed counts of 105, 85, 105,
95, and 110 for types 1, 2, 3, 4, and 5, respectively.
Type
1
2
3
4
5
Number
105
85
105
95
110
Assume we want to use a 0.05 significance level to test the claim that the four types are equally
popular.
(a) Identify the null hypothesis and the alternative hypothesis.
(b) Determine the test statistic. Show all work.
(c) Determine the P-value. Show all work.
(d) Is there sufficient evidence to support the manager’s claim that the five types are equally
popular? Justify your answer.
20.
A study of 8 different weight loss programs involved 200 subjects. Each of the 8 programs had
25 subjects in it. The subjects were followed for 12 months. Weight change for each subject was
recorded. We want to test the claim that the mean weight loss is the same for the 8 programs.
(a) Complete the following ANOVA table with sum of squares, degrees of freedom, and
mean square (Show all work):
Source of
variation
Factor
(Between)
Error
(Within)
Sum of Squares
(SS)
Total
620.05
Degrees of
freedom (df)
Mean Square
(MS)
199
N/A
50.8
(b) Determine the test statistic. Show work.
(c) Determine the P-value. Show work.
(d) Is there sufficient evidence to support the claim that the mean weight loss is the same for
the 8 programs at the significance level of 0.05? Explain.
…
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