mathematics

1. The sugar content of the syrup in canned peaches is normally distributed, and the variance is thought to be 218 (mg)2

(a) Test the hypothesis that the variance is not 18 (mg)2if a random sample of n = 10 cans yields a sample standard deviation of s = 4 mg, using a fixed-level test with 0.05. State any necessary assumptions about the underlying distribution of the data.

-Do part (a) using the 8 steps of rejection region approach. Also, don’t forget to state any necessary assumptions about the underlying distribution of the data.

(b) What is the P-value for this test?

(c) Find a 95% two-sided CI for

(d) Use the CI in part (c) to test the hypothesis.

(e) Conduct the same test as in part (a) using Minitab and attach the output.

(a) Construct normal probability plots for the two samples. Do these plots provide support of the assumptions of normality and equal variances? Why or why not? Also, attach the Minitab outputs for the normal probability plots.

(b) Do the data support the claim that the mean deflection temperature under load for type 1 pipe exceeds that of type 2? Use the 8 steps of the P-value approach with α=0.05.

(c) Conduct the test in part (b) by going through the last 4 steps of the critical region approach. Use α=0.05.

(d) Construct a 95% confidence interval for the difference in mean deflection temperatures. Explain how this interval confirms your finding in part (b).

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