# Interpretation of Statistical Tests

1. The statement that the probability of a Type I error is 0.05 means

1) alpha = 0.05

2) The probability that we are wrong in our decision of rejecting the null hypothesis is 5%.

3) All of the above

4) We decide to reject the null hypothesis at the 0.05 level of significance.

2. A gambler has developed two strategies for betting in the game of blackjack. To test these strategies, he decides to go gambling on a casino boat. He plays five sessions of blackjack with each strategy, with each session consisting of 20 hands. He then records the profits of each session. Please note that a negative profit indicates a loss. The computer output used in this analysis is shown below. The goal of the gambler is to determine, if possible, which of the two betting strategies will result in a higher mean profit.

TWO-SAMPLE T TESTS FOR PROFIT BY STRATEGY

NULL HYPOTHESIS: DIFFERENCE = 0

ALTERNATIVE HYP: DIFFERENCE < 0

Which of the following interpretations of the 95% confidence interval given above is correct?

1) At the 95% confidence level, we cannot determine which of the two strategies results in a higher mean profit.

2) We are 95% confident that the mean profit gained using strategy 2 exceeds the mean profit gained using strategy 1.

3) Since the interval contains only negative values, we are 95% confident that the mean profit of both strategies is negative.

4) We are 95% confident that the mean profit gained using strategy 1 exceeds the mean profit gained using strategy 2.

#### Solution Preview

1. The statement that the probability of a Type I error is 0.05 means

Type I error is a "false positive": it is incorrectly rejecting the null hypothesis when it is actually true. It is symbolized by the symbol alpha. All three statements listed are true, so the answer is (3).

2. A gambler has developed two strategies for betting in the game of blackjack. ...