I need help, on how to solve it.

1. An experimenter is interested in the hypothesis testing problem with H0: = 420 versus Ha: < 420, where is the average radiation level in a research laboratory. Suppose that a sample of 49 radiation level measurements is obtained and that the experimenter wishes to use =10.0 for the standard deviation of the radiation levels.

(a) What is the rejection region when =0.01?

(b) Suppose that the sample mean is 415.7. What would be the experimenter's decision of the hypothesis test based on the rejection region?

(c) What is the p-value for this hypothesis test?

3. For each of the following scenarios, state whether the null hypothesis should be rejected or not. State any assumptions that you make beyond the information that is given.

(a) H0: = 6, Ha: 6, n=25, x=5.6, s=2.5, =0.05

(b) H0: = 6, Ha: < 6, n=25, x=5.6, s=2.5, =0.05

(c) H0: = 25, Ha: > 25, n=81, x=26.4, s=3.2, =0.01

(d) H0: = 50, Ha: 50, n=55, p-value=0.053

4. An engineer selected 30 components at random and measure their strengths. 34,54,73,38,89,52,75,33,50,39,42,42,40,66,72,85,28,71,52,47,41,36,33,38,49,51,55,63,72,78

Does this data suggest that the population mean strength of the components differs from 50? Set up an appropriate hypothesis test to answer this question.