Chapter 8.1, Problem 13P

Basic Computation: Find Test Statistic, Corresponding P-value, and Conclude Test A random sample of size 20 from a normal distribution with σ = 4 produced a sample mean of 8.

1. (a) Check Requirements Is the $\bar{x}$ distribution normal? Explain.
2. (b) Compute the sample test statistic z under the null hypothesis H₀: μ = 7.
3. (c) For H₁: μ ≠ 7, estimate the P-value of the test statistic.
4. (d) For a level of significance of 0.05 and the hypotheses of parts (b) and (c), do you reject or fail to reject the null hypothesis? Explain.