Question

Jamie believes that a 9 ounce bag of potato chips does not really contain 9 ounces of chips. It is known that all potato chip bags are normally distributed with a standard deviation of 1 ounce. He wants to test this hypothesis at the 5% level of significance. He takes a sample of 40 bags of chips and finds the average amount of potato chips to be 10.5 ounces. What should Jamie’s conclusion be using the p-value approach? Be sure to show all six steps, including interpreting your answer in the context of the problem.

Answer 1

H₀: = 9

H₁: 9

The test statistic z = ()/()

                             = (10.5 - 9)/(1/)

                             = 9.49

P-value = 2 * P(Z > 9.49)

             = 2 * (1 - P(Z < 9.49)

             = 2 * (1 - 1)

             = 2 * 0 = 0

Since the P-value is less than the significance level(0 < 0.05), so we should reject the null hypothesis.

At 5% significance level,there is sufficient evidence to support Jamie's conclusion.