In the past the standard deviation of weights of certain 32.0 ozpackages filled

Question

In the past the standard deviation of weights of certain 32.0 ozpackages filled by a machine was 0.25 oz. A random sample of 20packages showed a standard deviation of 0.35 oz. Is the apparentincrease in variability significant at the 0.10 level ofsignificance? Assume package weight is normally distributed. (solvewith p value approach)
a. Symbolize the null and alternative hypothesis
b. Calculate the value of the statistic. Round to 2 places afterthe decimal point.
c. Find the p-value
d. At the 0.10 level of significance, there_____ enough evidence touggest a significant increase in variability

Explanation / Answer

H0: s^2 = ^2 Ha: s^2 does not equal ^2 Sample Standard Deviation: .35 --> Sample variance = .35^2 =.1225 Population standard deviation: .25 --> Population variance =.25^2 = .0625 Chi-Squared Test Test Statistic: x = (n-1)*s^2 / ^2 = (19)*.1225 / .0625 =37.24 Degrees of Freedom: n-1 = 19 --> p < .01 At the .1 significance level, we have a tail on either side of .1/2= .05. Thus, at the .1 significance level, since .01

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