Question

A certain brand of jelly beans are made so that each package contains about the same number of beans. The filling procedure is not perfect, however. The packages are filled with an average of 375 jelly beans, but the number going into each bag is normally distributed with a standard deviation of 8. You went to the store and purchased six bags of this brand of jelly beans in preparation for a Holiday party. You counted the number of jelly beans in these packages and found your six bags contained an average of 370 jelly beans. Is there any evidence to suggest that the bags are underfilled at 0.05 level? What is the p-value?

a.p=038.
b. Data is not normal; do not test.
c. p=.063.
d. p=.093

Answer 1

p=0.063

Explanation:

Let X be number of the certain brand of jelly beans that are made so that each package contains about the same number of beans.

X is N(375, 8)

YOu are collecting a sample size of

n = 8

Findings from the sample

`\bar x =370\\`

`H_0: \bar x =375\\H_a: \bar x <375`

(Left tailed test at 5% level)

Since sample size is small though sigma is known we use Z test, since norm

Mean difference = -5

Std error =
`(8)/(√(8) ) =2.828`

Test statistic t = mean diference / std error =
`(-5)/(2.828) \\=-1.768`

df = n-1 =5

p value = 0.063