Question

A company produces soda.  The company produces four varieties of the soda.

The company purchased a new bottling machine.  When the machine is working properly, bottles are filled with a normally-distributed process, with mean = 12.7 oz and var = .05 oz².

To test if working properly a sample of 25 bottles is taken and its fill levels are measured.  Data is normally distributed with the var = 05 oz²and sample mean = 12.6oz.

(a)is it fair to say the sample mean is less than 12.7 fluid ounces, given a one-sided hypothesis test and a significance level of .01?

(b)  What is the p-value associated with the value of the test statistic in part a?

(c)  Complete part a. but instead under the condition that the variance is unknown, estimate the unknown variance by using the sample variance of .06 ounces².

(d) Complete part a but under the assumption that instead of defining a significance level and determining an associated rejection region, the null hypothesis will be rejected if the sample mean is less than 12.65 fluid ounces. What is the probability of making a Type I error?

Answer 1

The population standard deviation is

(a)

Conclusion: We cannot conclude that the sample mean is less than 12.7 fluid ounces.

(b)

The p-value is 0.0125

(c)

(d)

The z-score for is

The required level of significance is