Download Practice problems on hypothesis testing

Practice problems on hypothesis tests
Multiple choice (only one answer is correct for each)
1) A brake light that has been in use a long time is known to have a mean reaction time of
0.8 seconds. A new brake light is tried out on a random sample of 50 drivers. A 95%
confidence interval for the mean reaction time for the new light (is (0.68, 0.76)
seconds. We are interested in seeing if the two lights are different in terms of mean
reaction time. Which of the following is a correct statement?
a) The null hypothesis is that the two light means are different.
b) The null hypothesis is that 
c) The alternative hypothesis is that 
d) The null hypothesis is that 
e) The null hypothesis is that 
2) Refer to question1. Which of the following is correct? (Better means shorter mean
reaction time.)
a) We will reject the null hypothesis and conclude the new light is better.
b) We will reject the null hypothesis and conclude the new light is worse.
c) We will reject the null hypothesis but cannot say if the new light is better or worse.
d) We will fail to reject the null hypothesis and conclude the new light is better.
e) We will fail to reject the null hypothesis and conclude the new light is worse.
3) Refer to question 1. Which of the following is correct?
a) We have made a Type I error.
b) We might have made a Type I error.
c) We have made a Type II error.
d) We might have made a Type II error.
e) We have made no errors.
5) We carry out a test of H0: 1=2 against H1: 1  2, at the significance level of 0.05,
and obtain a P-value of 0.03. Which of the following statements is TRUE?
a.
b.
c.
d.
e.
We have proven the null hypothesis must be true.
Since 0.03 < 0.05, we reject H0.
Since 0.03 < 0.05, we fail to reject H0.
There is not enough information to decide whether to reject H0 or not .
The probability H0 is true is 0.03.
6) A pain reliever that has been in use a long time takes 20 minutes on average to be effective. A new pain reliever is tried out on a random sample of 15 patients with postoperative pain. The mean time to relief for these patients is 17.3 minutes with a sample
standard deviation of 2.5 minutes. A 5% significance test is to be performed to determine
if the mean time for relief for the new painkiller is different from 20 minutes. The calculated value of the test statistic (t) and the critical value from the table (t*) respectively
are:
a.
b.
c.
d.
e.
(2.36, 2.262)
(4.18, 2.145)
(16.17, 2.145)
(16.17, 1.761)
(4.18, 1.960)
7) Suppose I am very concerned about Type I errors in a testing problem. Which of the
following are false statements?
a)
b)
c)
d)
e)
The significance level is the chance of a Type I error.
If I make Type I errors more likely, I will also make Type II errors more likely.
If I make Type I errors more likely, I will make Type II errors less likely.
A confidence interval of 98% will give a significance level of 2%.
I should use a high confidence level.
True/False
8) Each of the following statements is either True or False. Indicate which by circling the
letter T or the letter F. Do not give any explanation. If a statement is sometimes true and
sometimes false, then we will call it FALSE (ie it is only true if it is ALWAYS true).
(a) T F Failing to reject the null hypothesis implies the null hypothesis must be true.
(b) T F If you reject a null at a significance level of 1%, you must also reject at a level of 5%.
(c) T F If you reject a null hypothesis test, you have made a Type I error
(d) T F When we fail to reject a null hypothesis we could have made a Type II error.
(e) T F Suppose a 98% confidence interval for an unknown difference in two
means 1 - 2 is (0.35, 0.48). If we test H0: 1=2 against H1: 1  2 at the 2%
level, we reject H0.
(f) T F We carry out a hypothesis test H0: p1 = p2, which we fail to reject. This
proves that p1=p2.
(g) T F If we carry out a test at a significance level of 5%, and the P-value is 0.06,
we fail to reject the null hypothesis.