Question

Granola Crunch cereal is packaged in 1 pound boxes. Susan Torres, a quality control analyst who works for the manufacturer of the cereal, wants to check if the packaging process is working improperly: boxes are being over-filled or under-filled. A sample of 40 cereal boxes of Granola Crunch yields a mean weight of 1.02 pounds of cereal per box. Assume that the weight is normally distributed with a population standard deviation of 0.04 pound. Conduct a hypothesis test at the 5% significance level.

Specify the relevant null and alternative hypotheses; Calculate the test-statistic Find the p-value; State conclusion: do you reject H0? Determine whether quality control is failed; Give a 90% confidence interval for the mean weight of boxes of Granola Crunch cereal time for all drivers.

Answer 1

Ho : mu = 1

Ha: mu <> 1

TS = (Xbar - mu)/(Sigma /sqrt(n))

TS = 3.162 > critical value (1.96)

hence we reject the null hypothesis

we conclude that there is evidence that the packaging process is working improperly

p-value = 2 P(Z > |TS|) = 0.002

90% CI is (Xbar+ -z * sigma/sqrt(n))

z = 1.645

90% CI is (1.0096,1.0304)

Please give me a thumbs-up if this helps you out. Thank you! :)