Question

1. In testing the null hypothesis that p = 0.3 against the alternative that p not equal 0.3, the probability of a Type II error is _____________ when p = 0.4 than when p = 0.6.

a. the same

b. smaller

c. larger

d. none of the above

2. During the pre-flight check, Pilot Jones discovers a minor problem - a warning light indicates that the fuel guage may be broken. If Jones decides to check the fuel level by hand, it will delay the flight by 45 minutes. If Jones decides to ignore the warning, the aircraft may run out of fuel before it gets to Gimli. In this situation, what would be:

i) the appropriate null hypothesis? and;
ii) a type I error?

Question 2 options:

	a. Null Hypothesis: assume that the warning can be ignored. Type I error: decide to check the fuel by hand when there is in fact enough fuel.
	b. Null Hypothesis: assume that the warning can be ignored. Type I error: decide to ignore the warning when there is in fact not enough fuel.
	c. Null Hypothesis: assume that the fuel should be checked by hand. Type I error: decide to ignore the warning when there is in fact not enough fuel.
	d.Null Hypothesis: assume that the fuel should be checked by hand. Type I error: decide to check the fuel by hand when there is in fact enough fuel.
	e.Null Hypothesis: assume that the aircraft is already late. Type I error: taking a commercial flight to Gimli in the first place. 3. Failure to reject the null hypothesis means: a. acceptance of the alternative hypothesis. b. rejection of the null hypothesis. c. rejection of the alternative hypothesis. d. absolute acceptance of the null hypothesis. e.none of the above. 4. If the null hypothesis is false, increasing the level of significance for a specified sample size will increase the probability of rejecting the null hypothesis. a. True b. False

Answer 1

1. In testing the null hypothesis that p = 0.3 against the alternative that p not equal 0.3, the probability of a Type II error is _____________ when p = 0.4 than when p = 0.6.

Small.

2. During the pre-flight check, Pilot Jones discovers a minor problem - a warning light indicates that the fuel guage may be broken. If Jones decides to check the fuel level by hand, it will delay the flight by 45 minutes. If Jones decides to ignore the warning, the aircraft may run out of fuel before it gets to Gimli. In this situation, what would be:

Answer : Null Hypothesis: assume that the warning can be ignored.
Type I error: decide to check the fuel by hand when there is in fact enough fuel.

3. Failure to reject the null hypothesis means:

Answer : rejection of the alternative hypothesis.

4. If the null hypothesis is false, increasing the level of significance for a specified sample size will increase the probability of rejecting the null hypothesis.

False.

Because for fixed sample size, the smaller we specify the significance level (alpha), the larger will be the probability (beta) of not rejecting a false hypothesis.