Question

1.

a. In hypothesis testing when is a two-tail test used in lieu of a one-tail test and why?

b. In hypothesis testing when is the "t test" used rather than the "Z test"?

2.

a. If the question asks "is there evidence that the average price of gas is greater than some value ‘A’ is this a one-tail or two-tail test and why? What would your null and alternative hypothesis be and why?

b. What is the distinction between a Type 1 error and a Type 2 error?

Answer 1

1.a. Suppose a new drug is manufactured and we want to test its effectiveness against the current drug. We may use the one-tailed test since it maximizes the chances of detecting the improvement.. However there is a possibility of missing the fact that the new drug is originally less effective than the present dug.. Hence we should choose the one-tailed test if  effect of other side is negligible, If we have no idea then we use two tail test where a hypothesis does not include a directional relationship.

b. When we interest to test the population mean and sample comes from independently normal population and if population variance is unknown then we use t test instead of Z test.

2. a. One tail test (since we want to test whether  there is evidence that the average price of gas is greater than some value ‘A’).

Null hypothesis:  The average price of gas is less than equal to some value ‘A’

Alternative hypothesis: The average price of gas is greater than some value ‘A’.

b. Type I error: We reject null hypothesis when null hypothesis is true.

Type II error: We accept null hypothesis when null hypothesis is false.

Generally Type I error is more serious than Type II error. The upper bound of probability of Type I error is level of significance and 1-P(Type II error)=power of a test.