1) We test the null hypothesis H₀: μ = 10 and the alternative H_a: μ ≠ 10 for a normal population with σ = 4. A random sample of 16 observations is drawn from the population and we find the sample mean of these observations is x = 12. The P-value is closest to:

a) 0.9772

b) 0.4886

c) 0.0228

d) 0.0456

2) A certain population follows a normal distribution with mean μ and standard deviation σ = 2.5. You collect data and test the hypotheses

H₀: μ = 1, H_a: μ ≠ 1.

You obtain a P-value of 0.022. Which of the following is true?

a) A 95% confidence interval for μ will include the value 0

b) A 95% confidence interval for μ will include the value 1

c) A 99% confidence interval for μ will include the value 1

d) A 99% confidence interval for μ will include the value 0