# Hypothesis Testing Sample Questions

1. Measurements of the left handed and right handed gripping strengths of twelve left handed persons are recorded as follows.

PERSON 1 2 3 4 5 6 7 8 9 10 11 12

LEFT HAND 140 90 125 130 95 121 85 97 131 110 98 109

RIGHT HAND 138 87 110 132 96 120 86 90 129 100 101 117

We wish to test whether left handed persons have greater gripping strength in their dominant (left) hand. Assume normality of the appropriate population(s).

1a) What is the observed value of the test statistic?

Answer

a. .39

b. 1.17

c. 2.08

d. 3.16

1b) How many degrees of freedom does the test statistic have, under the null hypothesis?

Answer

a. 9

b. 10

c. 11

d. 20

1c) What is the p-value for these data?

Answer

a. <.01

b. .01-.05

c. .05-.10

d. >.10

1d) Find a 95% confidence interval for the difference in left and right hand gripping strength.

Answer

a. (-.31, 7.51)

b. (.03,7.17)

c. (-8.75, 15.95)

d. (-14.9,22.1)

e. (-1.84, 6.00)

2. A test of null hypothesis Ho vs the alternative Ha has p-value .047. Will the null hypothesis be rejected when the test is at level alpha=.05?

Answer

a. yes

b. no

3. Two spreadsheet programs (A and B) are compared to see which is easier to use. 10 students in the Faculty of Management were given a standard set of finance problems to solve using Program A and 16 students from the faculty were told solve the same problems using Program B. For each student, the total time taken to complete all the problems is recorded. The times for the students using Program A had mean 51.5 minutes and standard deviation 10.46 minutes; for Program B the mean was 38.0 minutes and the standard deviation 8.67 minutes.

3a) What is the pooled variance Sp**2 for these data? (Note: the notation Sp**2 means the square of Sp)

Answer

a. 8.62

b. 9.36

c. 9.57

d. 88.01

e. 81.24

f. 88.34

g. 92.29

4. The study in problem 4 was repeated in the Faculty of Science. Samples of size 10 and 15 were used for program A and program B. In this case the mean time for the students using program A was 52 minutes, and the mean time for students using program B was 42 minutes. The pooled standard deviation s_p was equal to 9 minutes. Using this faculty of Science data, test the alternative hypothesis that the mean time for program B is less than the mean time for program A.

4a) What is the value of the test statistic?

Answer

a. 0.12

b. 1.11

c. 2.72

d. 6.84

e. 10.0

4b) How many degrees of freedom does the test statistic have under the null hypothesis?

Answer

a. 10

b. 13

c. 16

d. 23

e. 25

f. 24

4c) What is the p-value for the test?

Answer

a. < .01

b. .01-.05

c. .05-.10

d. > .10

4d) Find a 95% confidence interval for the difference in population mean completion times between Program A and Program B.

Answer

a. (2.42, 17.58)

b. (5.5, 14.5)

c. (8.15, 11.85)

d. (8.18, 11.82)

e. (-0.31, 20.31)

5. If a test rejects Ho: mu = mu_0 in favour of Ha: mu not = mu_0 at level alpha, then the test will also reject Ho in favour of Ha: mu > mu_0 at level alpha.

Answer

a. true

b. false

c. insufficient information to decide

6. In testing for a difference between a new and old production process, the null hypothesis states that the new process is at least as good as the old one. A type I error is committed if:

Answer

a. It is concluded that the new process is at least as good when in fact, it is not.

b. It is concluded that the old process is better when in fact, it is.

c. It is concluded that the old process is better when in fact, it is not.

d. It is concluded that the new process is at least as good when in fact, it is.

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#### Solution Preview

I have answered all of your questions in the attached MS Word doc.

1. Measurements of the left handed and right handed gripping strengths of twelve left handed persons are recorded as follows.

PERSON 1 2 3 4 5 6 7 8 9 10 11 12

LEFT HAND 140 90 125 130 95 121 85 97 131 110 98 109

RIGHT HAND 138 87 110 132 96 120 86 90 129 100 101 117

We wish to test whether left handed persons have greater gripping strength in their dominant (left) hand. Assume normality of the appropriate population(s).

Since there are two groups ( Group #1 is "Left Hand Gripping Strength and Group #2 is "Right Hand Gripping Strength") with each person supplying one observation for each group this is a Dependent Samples T-Test on the Difference Between Means, sometimes also referred to as a Paired samples T-Test on the Difference Between Means.

1a) What is the observed value of the test statistic?

Answer

a. .39

b. 1.17

c. 2.08

d. 3.16

By calculating all of the differences between corresponding observations in the two groups (so the first value in the Left Hand group (the 140) minus the first value in the Right Hand group (the 138), and the second value of the Left Hand group (the 90) minus the second value of the Right Hand group (the 87), and so on) you can calculate the sample mean (represented by ) for the 12 differences. If you do this you'll find that = 2.08333, and . The formula for the Test Statistic in this hypothesis test is:

. So the best answer is "b. 1.17".

1b) How many degrees of freedom does the test statistic have, under the null hypothesis?

Answer

a. 9

b. 10

c. 11

d. 20

The formula for the df in a Paired Samples T-Test on the Difference of Two Means is , so in this problem we have . There are 11 df, so the correct answer is "c. 11".

1c) What is the p-value for these data?

Answer

a. <.01

b. .01-.05

c. .05-.10

d. >.10

Since we are interested in testing "whether left handed persons have greater gripping strength in their dominant (left) hand" we would be using the one-tailed, upper-tailed alternative hypothesis: . With such an alternative the formula for the P-Value is , which in this case (with 11 df) would be , ...

#### Solution Summary

The expert examines hypothesis testing and sample questions.