For each of the following situations, state whether a Type I, a Type II, or neither error has been made.
a) A test of H0: p = 0.6 vs. HA: p < 0.6 fails to reject the null hypothesis. Later it is discovered that p = 0.7.
b) A test of H0: μ = 30 vs. HA: μ > 30 rejects the null hypothesis. Later it is discovered that μ = 29.9.
c) A test of H0: p = 0.4 vs. HA: p /= 0.4 rejects the null hypothesis. Later it is discovered that p = 0.55.
d) A test of H0: p = 0.7 vs. HA: p < 0.7 fails to reject the null hypothesis. Later it is discovered that p = 0.6.

Step-by-step explanation:

a) A test of H0: p = 0.6 vs. HA: p < 0.6 fails to reject the null hypothesis. Later it is discovered that p = 0.7.

No error has been made since there is not enough statistical evidence to reject the null.

b) A test of H0: μ = 30 vs. HA: μ > 30 rejects the null hypothesis. Later it is discovered that μ = 29.9.

A type I error has been made. Rejecting the null hypothesis when it is actually true.

c) A test of H0: p = 0.4 vs. HA: p /= 0.4 rejects the null hypothesis. Later it is discovered that p = 0.55.

A type I error has been made since the p value was greater than 0.4, one will fail to reject the null but in the case the null was rejected.

d) A test of H0: p = 0.7 vs. HA: p < 0.7 fails to reject the null hypothesis. Later it is discovered that p = 0.6.

A type II error has been made since the p value is less than 0.7 and it was expected that the null should be rejected but that ws not the case.

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