Question

4) The time (in number of days) until maturity of a certain variety of hot pepper is Normally distributed, with mean μ and standard deviation σ = 2.4. This variety is advertised as taking 70 days to mature. I wish to test the hypotheses H0: μ = 70, Ha: μ > 70, so I select a simple random sample of four plants of this variety and measure the time until maturity. The four times, in days, are
76 73 69 70
Based on the data
A) I would reject H0 at level 0.10 but not at level 0.05. B) I would reject H0 at level 0.05 but not at level 0.01. C) I would reject H0 at level 0.01.
D) None of the above

Answer 1

P value = P(Z>1.667) = 0.0478

for = 0.05

p=0.0478<0.05, it is concluded that the null hypothesis(H0) is rejected.

for = 0.01

p=0.0478>0.01, it is concluded that the null hypothesis(H0) is not rejected.

B) I would reject H0 at level 0.05 but not at level 0.01