Deck 11: Hypothesis Testing for Single Populations

Question 1

Whenever hypotheses are established such that the alternative hypothesis is " $\textbf{ not }$ equal to", the hypothesis test would be a two-tailed test.

Answer 1

True

Question 2

A university wants to increase its retention rate of 4% for graduating students from the previous year. The null and alternative hypotheses to test if retention rate did increase will be?

A) H₀: $\pi$ $\le$ 0.04; H_a: $\pi$ > 0.04
B) H₀: $\pi$$≥$ 0.04; H_a: $\pi$ < 0.04
C) H₀: $\pi$ = 0.04; H_a: $\pi$ $\neq$ 0.04
D) H₀: $\pi$ > 0.04; H_a: $\pi$ $\le$ 0.04
E) H₀: $\pi$ $\neq$ 0.04; H_a: $\pi$ = 0.04

Answer 2

H₀: $\pi$ $\le$ 0.04; H_a: $\pi$ > 0.04

Question 3

Whenever hypotheses are established such that the alternative hypothesis is ">", then this would be a two-tailed test.

Answer 3

False

Question 4

Power is equal to (1 - $\beta$ ), the probability of a test rejecting the null hypothesis that is indeed $\textbf{ false. }$

Question 5

If the p value for a hypothesis test is 0.0271, which would be a correct decision?

A) Do not reject the null hypothesis when alpha is 0.10.
B) Do not reject the null hypothesis when alpha is 0.05.
C) Reject the null hypothesis when alpha is 0.025.
D) Reject the null hypothesis when alpha is 0.10.
E) none of the above

Question 6

Hypotheses are tentative explanations of a principle operating in nature.

Question 7

If the chosen significant level is 5%, then there is a

A) 10% probability of rejecting a false null hypothesis.
B) 10% probability of rejecting a true null hypothesis.
C) 5% probability of rejecting a false null hypothesis.
D) 5% probability of rejecting a true null hypothesis.
E) none of the above

Question 8

When a researcher fails to reject a $\textbf{ false }$ null hypothesis, a Type II error has been committed.

Question 9

The probability of committing a Type I error is called the power of the test.

Question 10

The first step in testing a hypothesis is to establish a true null hypothesis and a false alternative hypothesis.

Question 11

When a $\textbf{ false }$ null hypothesis is rejected, the researcher has made a Type II error.

Question 12

In testing hypotheses, the researcher initially assumes that the alternative hypothesis is true and uses the sample data to reject it.

Question 13

The rejection and non-rejection regions are divided by a point called the critical value.

Question 14

The null and the alternative hypotheses must be mutually exclusive and collectively exhaustive.

Question 15

The null hypothesis makes claim about a

A) population parameter.
B) sample statistics.
C) Type I error.
D) Type II error.
E) sample mean.

Question 16

If a null hypothesis was $\textbf{ not }$ rejected at the 0.10 level of significance, it will be rejected at a 0.05 level of significance based on the same sample results.

Question 17

If the researcher computes the probability of the calculated statistic and compares it to alpha, the level of significance to reach a decision, the researcher is using the p value method for testing the hypotheses.

Question 18

The rejection region for a hypothesis test becomes smaller if the level of significance is changed from 0.01 to 0.05.

Question 19

When a true null hypothesis is rejected, the researcher has made a Type I error.

Question 20

Generally speaking, the hypotheses that business researchers want to prove are stated in the alternative hypothesis.

Question 21

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 $\alpha$ =.05. If the sample mean is 58 and the population standard deviation is 16, the observed z value is ___.

A) -1
B) 1
C) -8
D) 8
E) 58

Question 22

A researcher is testing a hypothesis of a single mean. The critical z value for $\alpha$ =.05 and a two-tailed test is ±1.96. The observed z value from sample data is 2.85. The decision made by the researcher based on this information is to ___ the null hypothesis.

A) reject
B) not reject
C) redefine
D) change the alternate hypothesis into
E) restate the null hypothesis

Question 23

In a two-tailed hypothesis about a population mean with a sample size of 100 and α = 0.05, the rejection region would be ___.

A) z > 1.64
B) z > 1.96
C) z < -1.96 and z > 1.96
D) z < -1.64 and z > 1.64
E) z < -2.33 and z > 2.33

Question 24

In performing a hypothesis test where the null hypothesis is that the population mean is 23 against the alternative hypothesis that the population mean is $\textbf{ not }$ equal to 23, a random sample of 17 items is selected. The sample mean is 24.6 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 ___.

A) 17
B) 16
C) 15
D) 2
E) 1

Question 25

Jennifer Cantu, VP of Customer Services at Tri-City Auto Insurance Inc., monitors the claims processing time of the claims division. Her standard includes "a mean processing time of 5 days or less." Each week, her staff checks for compliance by analyzing a random sample of 60 claims. Jennifer's null hypothesis is ___.

A) $\mu$ > 5
B) $\sigma$ > 5
C) n = 60
D) $\mu$ < 5
E) $\mu$ = 5

Question 26

Consider the following null and alternative hypotheses:
H₀: µ $\le$ 67
H_a: µ > 67
These hypotheses ___.

A) indicate a one-tailed test with a rejection area in the right tail
B) indicate a one-tailed test with a rejection area in the left tail
C) indicate a two-tailed test
D) are established incorrectly
E) are not mutually exclusive

Question 27

If the alternative hypothesis states that the mean is $\textbf{ not }$ 40 kg, what is the rejection region for the hypothesis test?

A) both tails
B) lower or left tail
C) upper or right tail
D) centre
E) no tail

Question 28

Suppose you are testing the null hypothesis that a population mean is less than or equal to 80, against the alternative hypothesis that the population mean is greater than 80. If the sample size is 49 and alpha =.10, the critical value of z is ___.

A) 1.645
B) -1.645
C) 1.28
D) -1.28
E) 2.33

Question 29

Consider the following null and alternative hypotheses:
H_o: µ = 67
H_a: µ $\neq$ 67
These hypotheses ___.

A) indicate a one-tailed test with a rejection area in the right tail
B) indicate a one-tailed test with a rejection area in the left tail
C) indicate a two-tailed test
D) are established incorrectly
E) are not mutually exclusive

Question 30

A researcher is testing a hypothesis of a single mean. The critical z value for $\alpha$ =.05 and a two-tailed test is ±1.96. The test statistic from sample data is -1.85. The decision made by the researcher based on this information is to ___ the null hypothesis.

A) reject
B) not reject
C) redefine
D) change the alternate hypothesis into
E) restate the null hypothesis

Question 31

Which of the following is not one of the eights steps in the hypothesis testing procedure?

A) State the null and alternative hypotheses.
B) Select a level of significance.
C) Formulate a decision rule.
D) Select a test statistic.
E) Select a level of .

Question 32

A researcher is testing a hypothesis of a single mean. The critical z value for $\alpha$ =.05 and a two-tailed test is ±1.96. The observed z value from sample data is -2.11. The decision made by the researcher based on this information is to ___ the null hypothesis.

A) reject
B) not reject
C) redefine
D) change the alternate hypothesis into
E) restate the null hypothesis

Question 33

In performing a hypothesis test where the null hypothesis is that the population mean is 4.8 against the alternative hypothesis that the population mean is $\textbf{ not }$ equal to 4.8, a random sample of 25 items is selected. The sample mean is 4.1 and the sample standard deviation is 1.4. It can be assumed that the population is normally distributed. The degrees of freedom associated with this are ___.

A) 25
B) 24
C) 26
D) 2
E) 1

Question 34

Suppose the alternative hypothesis in a hypothesis test is "the population mean is greater than 60." If the sample size is 80 and alpha =.01, the critical value of z is ___.

A) 2.575
B) -2.575
C) 2.33
D) -2.33
E) 2.45

Question 35

Suppose the alternative hypothesis in a hypothesis test is: "the population mean is less than 60." If the sample size is 50 and alpha =.05, the critical value of z is ___.

A) 1.645
B) -1.645
C) 1.96
D) -1.96
E) 2.05

Question 36

Suppose you are testing the null hypothesis that a population mean is less than or equal to 80, against the alternative hypothesis that the population mean is greater than 80. The sample size is 49 and alpha =.05. If the sample mean is 84 and the population standard deviation is 14, the observed z value is ___.

A) 2
B) -2
C) 14
D) -14
E) 49

Question 37

A company produces an item that is supposed to have a six centimetre hole punched in the centre. A quality control inspector is concerned that the machine which punches the hole is "out of control" (hole is too large or too small). In an effort to test this, the inspector is going to gather a sample punched by the machine and measure the diameter of the hole. The alternative hypothesis used to statistical test to determine if the machine is out of control is

A) the mean diameter is > 6 centimetres.
B) the mean diameter is < 6 centimetres.
C) the mean diameter is = 6 centimetres.
D) the mean diameter is ≠ 6 centimetres.
E) the mean diameter is ≥ 6 centimetres.

Question 38

Consider the following null and alternative hypotheses:
H_o: µ $\ge$ 67
H_a: µ < 67
These hypotheses ___.

A) indicate a one-tailed test with a rejection area in the right tail
B) indicate a one-tailed test with a rejection area in the left tail
C) indicate a two-tailed test
D) are established incorrectly
E) are not mutually exclusive

Question 39

In a two-tailed hypothesis about a population mean with a sample size of 100 and alpha = 0.10, the rejection region would be ___.

A) z > 1.64
B) z > 1.28
C) z < -1.28 and z > 1.28
D) z < -1.645 and z > 1.645
E) z < -2.33 and z > 2.33

Question 40

A researcher is testing a hypothesis of a single mean. The critical z value for $\alpha$ =.05 and an one?tailed test is 1.645. The test statistic from sample data is 1.13. The decision made by the researcher based on this information is to ___ the null hypothesis.

A) reject
B) not reject
C) redefine
D) change the alternate hypothesis into
E) restate the null hypothesis

Question 41

In performing a hypothesis test where the null hypothesis is that the population mean is 4.8 against the alternative hypothesis that the population mean is $\textbf{ not }$ equal to 4.8, a random sample of 25 items is selected. The sample mean is 4.1 and the sample standard deviation is 1.4. It can be assumed that the population is normally distributed. The observed t value for this problem is ___.

A) -12.5
B) 12.5
C) -2.5
D) -0.7
E) 0.7

Question 42

In performing hypothesis tests about the population mean, the population standard deviation should be used if it is known. If it is $\textbf{ not }$ known, which of the following statistical test should be used?

A) z test of a population mean
B) t test of a population mean
C) z test of a population proportion
D) $\chi$ ² test of a population variance
E) t test of a population proportion

Question 43

A political scientist wants to prove that a candidate is currently carrying more than 60% of the vote in the riding. She has her assistants randomly sample 200 eligible voters in the riding by telephone and only 90 declare that they support her candidate. The test statistic for this problem is ___.

A) -4.33
B) 4.33
C) 0.45
D) -.31
E) 2.33

Question 44

Suppose a researcher is testing a null hypothesis that $\mu$ = 61. A random sample of n = 36 is taken resulting in a sample mean of 63 and s = 9. The test statistic is ___.

A) -0.22
B) 0.22
C) 1.33
D) 8.08
E) 7.58

Question 45

The diameter of 3.5 centimetre discs is normally distributed. Periodically, quality control inspectors at Winnipeg Discs randomly select a sample of 16 discs. If the mean diameter of the discs is too large or too small the disc punch is shut down for adjustment; otherwise, the punching process continues. The null hypothesis is ___.

A) n $\neq$ 16
B) n = 16
C) $\mu$ = 3.5
D) $\mu$ $\neq$ 3.5
E) $\mu$ ≥ 3.5

Question 46

The diameter of 3.5 centimetre discs is normally distributed. Periodically, quality control inspectors at Winnipeg Discs randomly select a sample of 16 discs. If the mean diameter of the discs is too large or too small the disc punch is shut down for adjustment; otherwise, the punching process continues. The last sample showed a mean and standard deviation of 3.49 and 0.08 centimetres, respectively. Using $\alpha$ = 0.05, the appropriate decision is ___.

A) reject the null hypothesis and shut down the punch
B) reject the null hypothesis and do not shut down the punch
C) do not reject the null hypothesis and shut down the punch
D) do not reject the null hypothesis and do not shut down the punch
E) do nothing

Question 47

In performing hypothesis tests about the population mean, the population standard deviation should be used if it is known. If it is $\textbf{ not }$ known, a t test can be used to test the mean if ___.

A) the sample size is at least thirty
B) the sample is random
C) the population mean is known
D) the population is normally distributed
E) the population is chi-square distributed

Question 48

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 $\textbf{ not }$ 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 level of significance is selected as 0.05. The critical t value for this problem is ___.

A) 1.753
B) 2.947
C) 2.120
D) 2.131
E) 2.311

Question 49

A company believes that it controls more than 30% of the total market share for one of its products. To prove this belief, a random sample of 144 purchases of this product is contacted. It is found that 50 of the 144 purchased this company's brand of the product. If a researcher wants to conduct a statistical test for this problem, the test would be ___.

A) a one-tailed test
B) a two-tailed test
C) an alpha test
D) a finite population test
E) a finite sample test

Question 50

Consider the following null and alternative hypotheses:
H₀: π $\le$ 0.16
H_a: π > 0.16
These hypotheses ___.

A) indicate a one-tailed test with a rejection area in the right tail
B) indicate a one-tailed test with a rejection area in the left tail
C) indicate a two-tailed test
D) are established incorrectly
E) are not mutually exclusive

Question 51

The diameter of 3.5 centimetre discs is normally distributed. Periodically, quality control inspectors at Winnipeg Discs randomly select a sample of 16 discs. If the mean diameter of the discs is too large or too small the disc punch is shut down for adjustment; otherwise, the punching process continues. The last sample showed a mean and standard deviation of 3.55 and 0.08 centimetres, respectively. Using $\alpha$ = 0.05, the appropriate decision is ___.

A) reject the null hypothesis and shut down the punch
B) reject the null hypothesis and do not shut down the punch
C) do not reject the null hypothesis and shut down the punch
D) do not reject the null hypothesis and do not shut down the punch
E) do nothing

Question 52

Consider the following null and alternative hypotheses:
H₀: π = 0.16
H_a: π $\neq$ 0.16
These hypotheses ___.

A) indicate a one-tailed test with a rejection area in the right tail
B) indicate a one-tailed test with a rejection area in the left tail
C) indicate a two-tailed test
D) are established incorrectly
E) are not mutually exclusive

Question 53

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 $\textbf{ not }$ 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 test statistic for this problem is ___.

A) 0.05
B) 0.20
C) 0.33
D) 1.33
E) 1.43

Question 54

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 $\textbf{ not }$ 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 level of significance is selected as 0.05. The decision rule for this problem is to reject the null hypothesis if the observed t value is ___.

A) less than -2.131 or greater than 2.131
B) less than -1.761 or greater than 1.761
C) less than -1.753 or greater than 1.753
D) less than -2.120 or greater than 2.120
E) less than -3.120 or greater than 3.120

Question 55

Consider the following null and alternative hypotheses:
H₀: π $\ge$ 0.16
H_a: π < 0.16
These hypotheses ___.

A) indicate a one-tailed test with a rejection area in the right tail
B) indicate a one-tailed test with a rejection area in the left tail
C) indicate a two-tailed test
D) are established incorrectly
E) are not mutually exclusive

Question 56

In performing a hypothesis test where the null hypothesis is that the population mean is 4.8 against the alternative hypothesis that the population mean is $\textbf{ not }$ equal to 4.8, a random sample of 25 items is selected. The sample mean is 4.1 and the sample standard deviation is 1.4. It can be assumed that the population is normally distributed. The level of significance is selected to be 0.10. The critical t value for this problem is ___.

A) 1.318
B) 1.711
C) 2.492
D) 2.797
E) 3.227

Question 57

A company believes that it controls more than 30% of the total market share for one of its products. To prove this belief, a random sample of 144 purchases of this product is contacted. It is found that 50 of the 144 purchased this company's brand of the product. If a researcher wants to conduct a statistical test for this problem, the test statistic would be ___.

A) 0.05
B) 0.103
C) 0.35
D) 1.24
E) 1.67

Question 58

Ophelia O'Brien, VP of Consumer Credit of Credit First Banks (CFB), monitors the default rate on personal loans at the CFB member banks. One of her standards is "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. Ophelia's null hypothesis is ___.

A) π > 0.05
B) π = 0.05
C) n = 30
D) n = 500
E) n = 0.05

Question 59

A company believes that it controls more than 30% of the total market share for one of its products. To prove this belief, a random sample of 144 purchases of this product is contacted. It is found that 50 of the 144 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 ___.

A) the population proportion is less than 0.30
B) the population proportion is greater than 0.30
C) the population proportion is not equal to 0.30
D) the population mean is less than 40
E) the population mean is greater than 40

Question 60

The diameter of 3.5 centimetre discs is normally distributed. Periodically, quality control inspectors at Winnipeg Discs randomly select a sample of 16 discs. If the mean diameter of the discs is too large or too small the disc punch is shut down for adjustment; otherwise, the punching process continues. The last sample showed a mean and standard deviation of 3.49 and 0.08 centimetres, respectively. Using $\alpha$ = 0.05, the critical t values are ___.

A) -2.120 and 2.120
B) -2.131 and 2.131
C) -1.753 and 1.753
D) -1.746 and 1.746
E) -2.567 and 2.567

Question 61

In a statistical test of hypotheses, a Type II error is committed if

A) we reject the null hypothesis when, in fact, the null hypothesis is true.
B) we fail to reject the null hypothesis when, in fact, the null hypothesis is true.
C) we fail to reject the null hypothesis when, in fact, the null hypothesis is not true.
D) we reject the null hypothesis when, in fact, the null hypothesis is not true.
E) none of the above

Question 62

The manager of an insurance company wants to prove that the true average claim is actually higher than $1,800 originally set by the company. He randomly selected 40 claims and determined a sample mean of $1,950. Test the appropriate hypotheses at ? = 0.05 to determine if the insurance company should be concerned. Assume that the standard deviation of claims is $500.

Question 63

If is set at 10% and alpha is 0.01, then the power of the test is?

A) 0.10
B) 0.90
C) 0.67
D) 0.01
E) 0.99

Question 64

Ophelia O'Brien, VP of Consumer Credit of Credit First Banks (CFB), monitors the default rate on personal loans at the CFB member banks. One of her standards is "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 38 defaulted loans. Using $\alpha$ = 0.10, the appropriate decision is ___.

A) reduce the sample size
B) increase the sample size
C) reject the null hypothesis
D) do not reject the null hypothesis
E) do nothing

Question 65

The executives of CareFree Insurance Inc. feel that "a majority of our employees perceive a participatory management style at CareFree." A random sample of 200 CareFree employees is selected to test this hypothesis at the 0.05 level of significance. Eighty employees rate the management as participatory. The null hypothesis is ___.

A) n = 30
B) n = 200
C) π = 0.50
D) π < 0.50
E) n > 200

Question 66

Ophelia O'Brien, VP of Consumer Credit of Credit First Banks (CFB), monitors the default rate on personal loans at the CFB member banks. One of her standards is "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. Using
$\alpha$ = 0.10, the critical z value is ___.

A) 1.645
B) -1.645
C) 1.28
D) -1.28
E) 2.28

Question 67

An article in the Edmonton Journal about driving practices in Strathcona County, claimed that 48% of drivers did $\textbf{ not }$ stop at stop-sign intersections on county roads. A follow-up study of 800 drivers on the county roads showed that 360 did $\textbf{ not }$ stop at stop-sign intersections. At $\alpha$ = 0.05
, is there evidence to suugest that the proportion of drivers $\textbf{ not }$ stopping at stop-sign intersections has changed using the p value approach.

Question 68

Elwin Osbourne, CIO at GFS, Inc., suspects that at least 25% of email messages sent by GFS employees are $\textbf{ not }$ business related. A random sample of 300 email messages was selected to test this hypothesis at the 0.01 level of significance. Fifty-four of the messages were $\textbf{ not }$ business related. The null hypothesis is ____.

A) \mu = 0.25
B) n = 300
C) π < 0.25
D) π ≠ 0.25
E) π = 0.25

Question 69

The executives of CareFree Insurance, Inc. feel that "a majority of our employees perceive a participatory management style at CareFree." A random sample of 200 CareFree employees is selected to test this hypothesis at the 0.05 level of significance. Ninety employees rate the management as participatory. The appropriate decision is ___.

A) do not reject the null hypothesis
B) reject the null hypothesis
C) reduce the sample size
D) increase the sample size
E) maintain status quo

Question 70

Ophelia O'Brien, VP of Consumer Credit of Credit First Banks (CFB), monitors the default rate on personal loans at the CFB member banks. One of her standards is "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. Using $\alpha$ = 0.10, the appropriate decision is ___.

A) reduce the sample size
B) increase the sample size
C) reject the null hypothesis
D) do not reject the null hypothesis
E) do nothing

Question 71

Elwin Osbourne, CIO at GFS, Inc., suspects that at least 25% of email messages sent by GFS employees are $\textbf{ not }$ business related. A random sample of 300 email messages was selected to test this hypothesis at the 0.01 level of significance. Sixty of the messages were $\textbf{ not }$ business related. The appropriate decision is ___.

A) increase the sample size
B) gather more data
C) maintain status quo
D) do not reject the null hypothesis
E) reject the null hypothesis

Question 72

The executives of CareFree Insurance, Inc. feel that "a majority of our employees perceive a participatory management style at CareFree." A random sample of 200 CareFree employees is selected to test this hypothesis at the 0.05 level of significance. Eighty employees rate the management as participatory. The appropriate decision is ___.

A) do not reject the null hypothesis
B) reject the null hypothesis
C) reduce the sample size
D) increase the sample size
E) do nothing

Question 73

A null hypothesis is π ≥ 0.65. To test this hypothesis, a sample of 400 is taken and alpha is set at 0.05. If the true proportion is π = 0.60, what is the probability of a Type II error?

A) 0.17
B) 0.45
C) 0.95
D) 0.67
E) 0.33

Question 74

A null hypothesis is π ≥ 0.65. To test this hypothesis, a sample of 400 is taken and alpha is set at 0.05. If the true proportion is π = 0.60, what is the power of the test?

A) 0.33
B) 0.45
C) 0.95
D) 0.67
E) 0.77

Question 75

Ophelia O'Brien, VP of Consumer Credit of Credit First Banks (CFB), monitors the default rate on personal loans at the CFB member banks. One of her standards is "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. Using $\alpha$ = 0.10, the test statistic is ___.

A) 1.03
B) -1.03
C) 0.046
D) -0.046
E) 1.33

Question 76

A null hypothesis is $\mu$ $\le$ 500. To test this hypothesis, a sample of 40 is taken and alpha is set at 0.01. If the true mean is 524 and population standard deviation is 115, what is the power of the test?

A) 0.16
B) 0.45
C) 0.67
D) 0.84
E) 0.99

Question 77

Elwin Osbourne, CIO at GFS, Inc., suspects that at least 25% of email messages sent by GFS employees are $\textbf{ not }$ business related. A random sample of 300 email messages was selected to test this hypothesis at the 0.01 level of significance. Fifty-four of the messages were $\textbf{ not }$ business related. The appropriate decision is __.

A) increase the sample size
B) gather more data
C) reject the null hypothesis
D) do not reject the null hypothesis
E) maintain status quo