1) We test the null hypothesis H0: μ = 10 and the alternative Ha: 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, Ha: 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