13.19 Testing software. You have computer .software that is supposed to generate observa tions from a standard Normal distribution. If this is true, the numbers generated come from a population with pi — 0 and a = I. A command to generate 100 observations gives outcomes with mean x = —0.2213. Assume that the population a remains fixed.

We want to test Hq: pi = 0 Hi'- Pt ¥=0

(a) Calculate the value of the z test statistic.

(b) Use Table C: is t: significant at the 5% level (a — 0.05)?

(c) Use Table C: is z significant at the 1% level (a — 0.01)?

(d) Between which two Normal critical values in the bottom row of Table C does Z lie? Between what two numbers does the P-value lie? Does the test give good evidence against the null hypothesis?