In a mechanical testing lab, Plexiglass strips are stretched to failure. Let X equal the change in length in mm before breaking. Assume that the distribution of X is N(μ, σ2). We shall test the null hypothesis H0: μ = 5.70 against the alternative hypothesis H1: μ > 5.70, using n = 8 observations of X.
(a) Define the test statistic and a critical region that has a significance level of α = 0.05. Sketch a figure showing this critical region.
(b) A random sample of eight observations of X yielded the following data:

Calculate the value of the test statistic and state your conclusion clearly.
(c) Give the approximate value of or bounds for the p-value of this test.

5.71 5.80 6.03 5.87 6.22 5.92 5.57 5.83