A manufacturer of candy must monitor the temperature at whic

A manufacturer of candy must monitor the temperature at which the candies
are baked. Too much variation will cause inconsistency in the taste of the candy. Past records show that
the standard deviation of the temperature has been 1.2oF . A random sample of 30 batches of candy is
selected, and the sample standard deviation of the temperature is 2.1oF .
a. (5 points) At the 0.05 level of significance, is there evidence that the population standard deviation
has increased above 1.2oF ?
b. (5 points) What assumption do you need to make in order to perform this test?
c. (5 points) Compute the p-value in (a) and interpret its meaning.

Please show detailed steps

Solution

a. (5 points) At the 0.05 level of significance, is there evidence that the population standard deviation has increased above 1.2oF ?

Ho: o= 1.2

Ha: o>1.2

The test statistic is

Chisquare= (n-1)*s^2/o^2

=(30-1)*2.1^2/1.2^2

=88.81

It is a right-tailed test.

The degree of freedom =n-1=30-1=29

Given a=0.05, the critical value of X^2 with 0.95 and df=29 is 42.56 (from chisquare table)

The rejection region is if X^2>42.56, we reject the null hypothesis.

Since 88.81 is larger than 42.56, we reject the null hypothesis.

So we can conclude that there is evidence that the population standard deviation has increased above 1.2oF

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b. (5 points) What assumption do you need to make in order to perform this test?

We need to assume that the population follows normal distribution.

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c. (5 points) Compute the p-value in (a) and interpret its meaning.

The p-value = P(X^2 with df=29 >88.81) =0 (from chisquare table)

Since the p-value is less than 0.05, we reject the null hypothesis.