Question
When we test H_0: mu = 0 against H_a: mu > 0, we get a P-value of 0 08. a. What would the decision be for a significance level of 0.05? Interpret in context. b. If the decision in (a) is in error, what type of error, what type of error is it? c. Suppose the significance level were instead 0.10. What decision would you make, and if it is in error, what type of error is it? a. What would the decision be for a significance level of 0.05? A. We would decide not to reject the null hypothesis. We would not have sufficient evidence that the population mean is different from 0. B. We would decide not to reject the null hypothesis. We would have sufficient evidence that the population mean is different from 0. C. We would decide to reject the null hypothesis. We would have sufficient evidence that the population mean is different from 0. D. We would decide to reject the null hypothesis. We would not have sufficient evidence that the population mean is different from 0. b. If the decision in (a) is in error, what type of error is it? Type II Type I c. What decision would you make and if it is in error what type of error is it? A. If the significance level were instead 0.10 we would decide to reject the null hypothesis. If this decision were in error it would be a Type II error.
Explanation / Answer
a. Since p-value = 0.08 > level of significance = 0.05, we fail to reject H0, i.e. there is not sufficient evidence that the population mean is different from 0. Hence Option (A) is the correct choice. (Ans).
b. If the decision in (a) is error then we will reject H0, when H0 is true. Hence it will be Type-I error. (Ans).
c.If the significance level is 0.10, then the p-value = 0.05 < level of significance = 0.10, then we reject H0, i.e. there is sufficient evidence that the population mean is different from 0.
If the decision is in error then we fail to reject H0, when H0 is false. Thus it is a Type-II error.
Hence Option (A) is the correct choice. (Ans).
