# Hypothesis testing MCQs

Question 1 Multiple Choice

In testing hypotheses, the researcher initially assumes:

the alternative hypothesis is true.

the null hypothesis is true

errors cannot be made

the population parameter of interest is known

Question 2 Multiple Choice

The rejection and non rejection regions are divided by the:

rejection value

dividing point

critical value

point of no return

Question 3 Multiple Choice

When a true null hypothesis is rejected, the researcher has committed a:

Type II error

Type I error

rejection error

error in judgment

Question 4 Multiple Choice

Whenever hypotheses are established such that the alternative hypothesis is ">", then the test is a:

Type I test

two-tailed test

one-tailed test

Type II test

Question 5 Multiple Choice

If a business researcher has a new theory about buying habits of consumers and wants to test it, the new theory usually is formulated into the:

null hypothesis

alternative hypothesis

critical value

substantive hypothesis

Question 6 Multiple Choice

Suppose the alternative hypothesis in a hypothesis test is "the population mean is greater than 65". If the sample size is 50 and alpha is .05, the critical value of z is:

1.645

-1.645

1.96

-1.96

Question 7 Multiple Choice

Suppose you are testing the null hypothesis that a population mean is greater than or equal to 60, against the alternative hypothesis that the population mean is less than 60. The sample size is 64 and alpha is .05. If the sample mean is 58 and the sample standard deviation is 16, the observed z value is:

1.00

1.00

8.00

2.16

Question 8 Multiple Choice

A business researcher has a theory that the average age of managers in a particular industry is over 35-years-old, and he wants to prove this. In conducting a statistical test on this theory, the null hypothesis would be:

the population mean is < 35

the population mean is 35

the population mean is = 35

the population mean is > 35

Question 9 Multiple Choice

A two-tailed hypothesis test about the mean is performed. The observed z value is 1.78. If alpha is 0.05, the correct decision would be:

fail to reject the null hypothesis

reject the null hypothesis

take a larger sample

not enough information to make a decision

Question 10 Multiple Choice

Suppose a business researcher conducts a hypothesis test and the observed z is positive. If the business researcher is conducting a one-tail test in the upper tail instead of a two-tail test, the table value that the researcher uses for the one-tail test would be what compared to the positive table value for the two-tail test?

The same

Larger

Smaller

None of the above

Question 11 Multiple Choice

A business researcher has conducted a hypothesis test and obtained an observed z value of 1.47. The p-value for this observed z is:

.0708

.0915

.2138

.4292

Question 12 Multiple Choice

In performing a hypothesis test where the null hypothesis is that the population mean is 45 against the alternative hypothesis that the population mean is not equal to 45, a random sample of 17 items is selected. The sample mean is 47.6 and the sample standard deviation is 3.3. It can be assumed that the population is normally distributed. The degrees of freedom associated with this are:

2

15

16

17

Question 13 Multiple Choice

In performing a hypothesis test where the null hypothesis is that the population mean is 6.9 against the alternative hypothesis that the population mean is not equal to 6.9, a random sample of 16 items is selected. The sample mean is 7.1 and the sample standard deviation is 2.4. It can be assumed that the population is normally distributed. The observed "t" value for this problem is:

.05

.20

.33

1.33

Question 14 Multiple Choice

The diameter of 3.5 inch diskettes is normally distributed. Periodically, quality control inspectors randomly select a sample of 23 diskettes. If the mean diameter of the diskettes is too large or too small the diskette punch is shut down for adjustment; otherwise, the punching process continues. The last sample showed a mean and standard deviation of 3.47 and 0.08 inches, respectively. Using α = 0.01, the appropriate decision is :

reject the null hypothesis and shut down the punch

reject the null hypothesis and do not shut down the punch

do not reject the null hypothesis and shut down the punch

do not reject the null hypothesis and do not shut down the punch

Question 15 Multiple Choice

A market researcher is testing consumer opinions about a new product. Consumers are asked to rate the product on a scale of from 0 to 10 as to whether or not they would purchase the product if it were available (where 0 = absolutely would not purchase, 10 = absolutely would purchase). Past studies have shown that this scale is normally distributed in the population. The market researcher will not give the go ahead for further development of the product unless the population mean purchase score is greater than 6.00. A sample of eight scores are obtained as follows: 7, 8, 5, 6, 9, 7, 5, 8. The observed t statistic is:

0.21

1.70

1.81

4.83

Question 16 Multiple Choice

A company believes that it controls more than 40% of the total market share for one of its products. To prove this belief, a random sample of 165 purchases of this product are contacted. It is found that 70 of the 165 purchased this company's brand of the product. If a researcher wants to conduct a statistical test for this problem, the alternative hypothesis would be:

the population proportion is not equal to 0.40

the population mean is equal to 0.40

the population proportion is less than 0.40

the population proportion is greater than 0.40

Question 17 Multiple Choice

A bank inspector monitors the default rate on personal loans at the AFB member banks. One standard that she examines is that no more than 5% of personal loans should be in default. On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. The bank inspector's alternate hypothesis is:

p> 0.05

p< 0.05

p = .05

P ≠ .05

Question 18 Multiple Choice

A bank inspector monitors the default rate on personal loans at the AFB member banks. One standard that she examines is that no more than 5% of personal loans should be in default. On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. If the bank inspector uses hypothesis testing techniques to test this and if alpha is .10, then the observed value is:

-1.03

1.03

-0.046

0.046

Question 19 Multiple Choice

Management at a large company has recently implemented a more participatory management style. Management believes that at least half of the company's employees feel that they are more a part of the decision making process than before. To test this, the company's business researcher randomly polls 180 company employees. One hundred and seven of those polled say that they feel they are more a part of the decision making process than before. Suppose the researcher is using a 1% level of significance. The observed value is:

2.67

2.53

1.84

1.56

Question 20 Multiple Choice

A business researcher is testing the following hypotheses using a 1% level of significance.

A sample of 671 is taken and the sample proportion is .38. The critical z value and observed z value are respectively:

2.575, 3.33

2.575, 3.11

2.33, 3.33

2.33, 3.11

Question 21 Multiple Choice

Suppose a business researcher wants to test the following hypotheses:

The researcher takes the following random sample from the population to conduct the test and assumes that the data come from a normally distributed population:

32 35 33 36 35 29

What is the observed value of chi-square for this hypothesis test?

3.33

7.12

11.04

14.23

Question 22 Multiple Choice

The Electrorist company manufactures a line of electrical resistors. Presently, the carbon composition line is producing 100 ohm resistors. The population variance of these resistors "must not exceed 3 sq. inches" to conform to industry standards. Periodically, the quality control inspectors check for conformity by randomly select 15 resistors from the line and calculating the sample variance. The last sample had a variance of 4.36. Using α = 0.05, the observed value of chi-square is.

29.57

21.80

20.35

19.76

Question 23 Multiple Choice

The human resources director of American First Banks (AFB), is reviewing the employee training programs of AFB banks. Based on a recent census of personnel, he knows that the variance of teller training time in the Southeast region is 8, and he wonders if the variance in the Southwest region is the same number. His staff randomly selected personnel files for 9 tellers in the Southwest Region, and determined that their mean training time was 25 hours and that the standard deviation was 4 hours. Using α = 0.10, the appropriate decision is:

increase the sample size

reduce the sample size

do not reject the null hypothesis

reject the null hypothesis

Question 24 Multiple Choice

A business researcher is conducting a one-tailed hypothesis test of the mean. The alternative hypothesis is that the mean is less than 27. A random sample of 36 is taken to test the hypothesis. The sample mean is 26 and the standard deviation is 5. Using an alpha of .05, the business researcher fails to reject the null hypothesis. If the population mean is actually 25, what is the probability of committing a type II error?

.1390

.1745

.2236

.2761

Question 25 Multiple Choice

A business researcher is testing to determine if a population proportion is more than .38. She takes a random sample of 480 and obtains a sample proportion of .40. Using an alpha of .10, if she decides to fail to reject the null hypothesis but the population proportion is actually .42, what is the probability of committing a type II error?

.0916

.1985

.3015

.6985

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#### Solution Summary

This posting contains solutions to following hypothesis testing MCQs

10 Hypothesis Testing MCQs

True or False: The probability of Type I error is referred to as the significance level of the test.

True

False

A Type II error is defined as:

rejecting a true null hypothesis.

rejecting a false null hypothesis.

failing to reject a true null hypothesis.

failing to reject a false null hypothesis.

Consider testing the hypotheses H0: mu = 50 vs. H1: mu does not equal 50.

If n = 64, mean = 53.5, and standard deviation = 10, then the value of the test statistic is:

z = 1.96.

t = 1.64.

z = 2.80.

t = 1.96.

z = 1.64

True or False: Failure to reject a null hypothesis constitutes proof that it is true.

True

False

In order to determine the p-value, which of the following is not needed?

The level of significance

Whether the test is one or two tail

The value of the test statistic

All of these are needed.

The p-value of a test is:

the smallest alpha at which the null hypothesis can be rejected.

the largest alpha at which the null hypothesis can be rejected.

the smallest alpha at which the null hypothesis cannot be rejected.

all of the above.

True or False: Reducing the probability of a Type I error also reduces the probability of a Type II error.

True

False

Suppose that we reject a null hypothesis at the .05 level of significance. Then for which of the following alpha values do we also reject the null hypothesis?

0.06

0.04

0.03

0.02

In testing the hypotheses H0: pi = 0.40, H1: pi > 0.40 at the 5% significance level, if the sample proportion is 0.45, and the standard error of the sample proportion is 0.035, the appropriate conclusion would be:

to reject H0.

not to reject H0.

to reject H1.

to reject both H0 and H1.

A professor of math refutes the claim that the average student spends 3 hours studying for the midterm exam. Which hypothesis is used to test the claim?

H0: mu does not equal 3, H1: mu > 3

H0: mu = 3, H1: mu does not equal 3

H0: mu does not equal 3, H1: mu = 3

H0: mu = 3, H1: mu < 3

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