Deck 22: What Is a Test of Significance

Question 1

If a significance test gives P-value 0.005,

A) the margin of error is 0.005.
B) the null hypothesis is very likely to be true.
C) we do not have good evidence against the null hypothesis.
D) we do have good evidence against the null hypothesis.
E) the effect of interest is practically significant.

Answer 1

we do have good evidence against the null hypothesis.

Question 2

A large company that produces a "fat-burner" pill claims an average loss of 20 pounds in the first month. A consumer advocacy group believes that this claim is actually just "hype" intended to sell more of the compound. The advocacy group would like to obtain statistical evidence about this issue and takes a random sample of 100 consumers who responded that they had purchased the pill but didn't know what the survey was about. They find that these 100 people lost an average of 18 pounds with a standard deviation of 7.5 pounds.
What are the null and alternative hypotheses in this situation?

A) H₀:  = 18 H_a:  < 18
B) H₀:  = 18 H_a:   18
C) H₀:  = 20 H_a:  < 20
D) H₀:  = 20 H_a:   20

Answer 2

H₀:  = 20 H_a:  < 20

Question 3

A scientist is studying the relationship between the depth of a watermelon vines' roots and the weight of the watermelons produced. The scientist collects measurements from a random sample of vines. He then conducts a significance test in which the null hypothesis is that there is no correlation between the two variables (correlation = 0) versus the alternative that the correlation is greater than 0. From this test he found a
P-value of 0.0032. What does this tell us?

A) There is significant evidence that the correlation is greater than 0 at the 0.05 level.
B) There is no significant evidence that the correlation is greater than 0 at the 0.05 level.
C) The correlation is very small.
D) The correlation is very close to 1.

Answer 3

There is significant evidence that the correlation is greater than 0 at the 0.05 level.

Question 4

A large company that produces a "fat-burner" pill claims an average loss of 20 pounds in the first month. A consumer advocacy group believes that this claim is actually just "hype" intended to sell more of the compound. The advocacy group would like to obtain statistical evidence about this issue and takes a random sample of 100 consumers who responded that they had purchased the pill but didn't know what the survey was about. They find that these 100 people lost an average of 18 pounds with a standard deviation of 7.5 pounds.
What is the P-value for this significance test?

A) 0.0228
B) 0.0045
C) 0.3947
D) 0.6093

Question 5

In a recent poll, 30 percent of adults said they wanted to "cut down or be free of gluten," according to The NDP Group, the market-research company that conducted the poll. A researcher wonders if a smaller proportion of students at her university would respond in the same fashion.
Suppose the researcher conducts a survey of a random sample of 25 students at her university and five of them say they want to at least reduce gluten. A statistician carries out a significance test of the null hypothesis that the proportion wanting to reduce gluten at the university is the same as for all adults versus the alternative hypothesis that a smaller proportion p of students would say they want to reduce or be free of gluten.
What is the P-value for this significance test?

A) less than 0.01
B) between 0.01 and 0.05
C) between 0.05 and 0.10
D) more than 0.10

Question 6

The null hypothesis is

A) another name for the alternative hypothesis.
B) true with 95% probability.
C) usually a statement of "no effect" or "no difference."
D) determined by looking at the data.
E) statistically significant.

Question 7

A paint manufacturer fills cans of paint using a machine that has been calibrated to fill the cans to contain an average  of 1 gallon (128 ounces) each. To test whether their machine has come out of calibration, the manufacturer takes a random sample of 25 cans and finds that they average 128.2 ounces with a standard deviation of 2 ounces. Is this strong evidence that the filling machine is set too high and thus is no longer calibrated properly?
What are the null and alternative hypotheses in this situation?

A) H₀:  = 128 H_a:  < 128
B) H₀:  = 128 H_a:  > 128
C) H₀:  = 128 H_a:   128
D) H₀:  = 128 H_a:  = 128.2

Question 8

In a recent poll, 30 percent of adults said they wanted to "cut down or be free of gluten," according to The NDP Group, the market-research company that conducted the poll. A researcher wonders if a smaller proportion of students at her university would respond in the same fashion.
Suppose the researcher conducts a survey of a random sample of 25 students at her university and five of them say they want to at least reduce gluten. A statistician carries out a significance test of the null hypothesis that the proportion wanting to reduce gluten at the university is the same as for all adults versus the alternative hypothesis that a smaller proportion p of students would say they want to reduce or be free of gluten.
What is the value of the standardized test statistic for this significance test?

A) 0.200
B) - 0.100
C) - 1.091
D) - 1.250

Question 9

A genetic theory says that a cross between two pink flowering plants will produce red flowering plants a proportion p = 0.25 of the time. To test the theory, 100 crosses are made and 31 of them produce a red flowering plant. Is this evidence that the theory is wrong?
What is the value of the standardized test statistic for this significance test?

A) -1.297.
B) 1.297.
C) -1.386.
D) 1.386.

Question 10

A large company that produces a "fat-burner" pill claims an average loss of 20 pounds in the first month. A consumer advocacy group believes that this claim is actually just "hype" intended to sell more of the compound. The advocacy group would like to obtain statistical evidence about this issue and takes a random sample of 100 consumers who responded that they had purchased the pill but didn't know what the survey was about. They find that these 100 people lost an average of 18 pounds with a standard deviation of 7.5 pounds.
What is the value of the standardized test statistic for this significance test?

A) -2.000
B) 0.267
C) -0.267
D) -2.667

Question 11

Among the findings of the American Religion Identification Survey (ARIS) of 1,710 college students in 2013 was their response to whether religion is the root cause of conflicts around the globe.
Asked whether religion brings more conflict than peace, 47 percent said Yes, 41 percent said
No, and 12 percent were unsure.
We might use these data to answer the question, "Do more than half of all college students think religion brings more conflict than peace?" To do this, we would take as our null hypothesis:

A) p < 0.5.
B) p = 0.5.
C) p > 0.5.
D) p  0.5.

Question 12

In a recent poll, 30 percent of adults said they wanted to "cut down or be free of gluten," according to The NDP Group, the market-research company that conducted the poll. A researcher wonders if a smaller proportion of students at her university would respond in the same fashion.
Suppose the researcher conducts a survey of a random sample of 25 students at her university and five of them say they want to at least reduce gluten. A statistician carries out a significance test of the null hypothesis that the proportion wanting to reduce gluten at the university is the same as for all adults versus the alternative hypothesis that a smaller proportion p of students would say they want to reduce or be free of gluten.
What are the null and alternative hypotheses in this situation?

A) H₀: p = 0.30 H_a: p < 0.30
B) H₀: p = 0.30 H_a: p  0.30
C) H₀: p = 0.30 H_a: p < 0.20
D) H₀: p = 0.20 H_a: p  0.30

Question 13

If the value of the standardized test statistic is 2.5,

A) conclude that the null hypothesis and the alternative hypothesis are the same.
B) we reject the null hypothesis at the 5% significance level.
C) we fail to reject the null hypothesis at the 5% significance level.
D) we reject the alternative hypothesis at the 5% significance level.
E) we should use a different null hypothesis.

Question 14

A genetic theory says that a cross between two pink flowering plants will produce red flowering plants a proportion p = 0.25 of the time. To test the theory, 100 crosses are made and 31 of them produce a red flowering plant. Is this evidence that the theory is wrong?
What are the null and alternative hypotheses in this situation?

A) H₀: p = 0.25 H_a: p > 0.25
B) H₀: p = 0.25 H_a: p  0.25
C) H₀: p = 0.31 H_a: p > 0.31
D) H₀: p = 0.31 H_a: p  0.31

Question 15

We would like to test the hypothesis that  = 20 versus the alternative that   20 using data from a random sample. We calculate the standardized test statistic to be 1.2. The P-value would then be

A) 0.8849.
B) 0.0240.
C) 0.1151.
D) 0.2302.

Question 16

The P-value of a test of significance is calculated assuming

A) the null hypothesis is true.
B) the alternative hypothesis is true.
C) nothing-we make no assumptions about which hypothesis is true in order to avoid bias.
D) a significance level of 0.05.

Question 17

If the P-value of a test of significance is 0.999 then

A) the null hypothesis is true.
B) the null hypothesis is false.
C) the null hypothesis provides a plausible explanation of the data.
D) the null hypothesis is true, and the null hypothesis provides a plausible explanation of the data.

Question 18

Among the findings of the American Religion Identification Survey (ARIS) of 1,710 college students in 2013 was their response to whether religion is the root cause of conflicts around the globe.
Asked whether religion brings more conflict than peace, 47 percent said Yes, 41 percent said
No, and 12 percent were unsure.
The P-value for the test in the previous question is about 0.99. This means that:

A) the poll gives very strong evidence that more than half of college students believe religion brings more conflict than peace.
B) the poll gives weak evidence that more than half of college students believe religion brings more conflict than peace .
C) the poll sheds no light on whether more than half of college students believe religion brings more conflict than peace.
D) the poll gives no evidence that more than half of college students believe religion brings more conflict than peace.

Question 19

If a significance test gives a P-value of 0.50,

A) the margin of error is 0.50.
B) the null hypothesis is very likely to be true.
C) we do not have good evidence against the null hypothesis.
D) we do have good evidence against the null hypothesis.
E) the effect of interest is practically significant.

Question 20

A genetic theory says that a cross between two pink flowering plants will produce red flowering plants a proportion p = 0.25 of the time. To test the theory, 100 crosses are made and 31 of them produce a red flowering plant. Is this evidence that the theory is wrong?
What is the P-value for this significance test?

A) 0.0808
B) 0.1616
C) 0.5000
D) 0.9192

Question 21

A paint manufacturer fills cans of paint using a machine that has been calibrated to fill the cans to contain an average  of 1 gallon (128 ounces) each. To test whether their machine has come out of calibration, the manufacturer takes a random sample of 25 cans and finds that they average 128.2 ounces with a standard deviation of 2 ounces. Is this strong evidence that the filling machine is set too high and thus is no longer calibrated properly?
What is the value of the standardized test statistic for this significance test?

A) -0.02.
B) 0.02.
C) 0.5.
D) -1.918.

Question 22

The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitude, and study habits of college students. Scores range from 0 to 200 and follow (approximately) a normal distribution with mean of 115 and standard deviation  = 25. You suspect that incoming freshman have a mean  which is different than 115, because they are often excited yet anxious about entering college. To test your suspicion, you test the hypotheses
H₀:  = 115 H_a:  115.
In testing these hypotheses, which of the following would be strong evidence against the null hypothesis?

A) using a small level of significance
B) using a large level of significance
C) obtaining data with a small P-value
D) obtaining data with a large P-value

Question 23

In a statistical test of hypotheses, we say the data are statistically significant at level  if

A)  = 0.05.
B)  is small.
C) the P-value is less than .
D) the P-value is larger than .

Question 24

A paint manufacturer fills cans of paint using a machine that has been calibrated to fill the cans to contain an average  of 1 gallon (128 ounces) each. To test whether their machine has come out of calibration, the manufacturer takes a random sample of 25 cans and finds that they average 128.2 ounces with a standard deviation of 2 ounces. Is this strong evidence that the filling machine is set too high and thus is no longer calibrated properly?
Based on the P-value for a significance test in this situation, we should conclude

A) the null hypothesis provides a reasonable explanation of the data.
B) the alternative hypothesis provides a reasonable explanation of the data.
C) we should reject the null hypothesis at significance level 0.05.
D) the alternative hypothesis provides a reasonable explanation of the data, and we should reject the null hypothesis at significance level 0.05.

Question 25

A city ordinance requires that more than 75% of its residents must agree to the construction of new public buildings (using tax dollars) before any such structures can be built. A proposal has been made to build a new recreational facility in the city, and sponsors of the proposal want to conduct a small survey to see if it would be approved if put to an official vote of all residents. A simple random sample of 150 residents revealed that 123 supported a change (and 27 did not).
What is the value of the standardized test statistic for this significance test?

A) -2.23.
B) 1.98.
C) 2.23.
D) 2.97.

Question 26

A city ordinance requires that more than 75% of its residents must agree to the construction of new public buildings (using tax dollars) before any such structures can be built. A proposal has been made to build a new recreational facility in the city, and sponsors of the proposal want to conduct a small survey to see if it would be approved if put to an official vote of all residents. A simple random sample of 150 residents revealed that 123 supported a change (and 27 did not).
What are the null and alternative hypotheses in this situation?

A) H₀:  = 112.5 H_a:  > 112.5
B) H₀:  = 112.5 H_a:   112.5
C) H₀: p = 0.75 H_a: p > 0.75
D) H₀: p = 0.75 H_a: p  0.75

Question 27

A paint manufacturer fills cans of paint using a machine that has been calibrated to fill the cans to contain an average  of 1 gallon (128 ounces) each. To test whether their machine has come out of calibration, the manufacturer takes a random sample of 25 cans and finds that they average 128.2 ounces with a standard deviation of 2 ounces. Is this strong evidence that the filling machine is set too high and thus is no longer calibrated properly?
What is the P-value for this significance test?

A) 0.0287
B) 0.3085
C) 0.5000
D) 0.6915
E) 0.9713

Question 28

A city ordinance requires that more than 75% of its residents must agree to the construction of new public buildings (using tax dollars) before any such structures can be built. A proposal has been made to build a new recreational facility in the city, and sponsors of the proposal want to conduct a small survey to see if it would be approved if put to an official vote of all residents. A simple random sample of 150 residents revealed that 123 supported a change (and 27 did not).
What is the P-value for this significance test?

A) 0.9861
B) 0.9773
C) 0.0227
D) 0.0139
E) 0.0013

Question 29

We would like to test the hypothesis that p = 0.5 versus the alternative that p < 0.5 using data from a random sample. We calculate the standard score to be -1.8. The P-value would then be

A) 0.9641.
B) 0.0359.
C) 0.5000.
D) 0.6915.
E) 0.3085.

Question 30

A university administrator obtains a sample of the academic records of past and present scholarship athletes at the university. The administrator reports that no significant difference was found in the mean GPA (grade point average) for male and female scholarship athletes (P-value = 0.287). This means that

A) the GPAs for male and female scholarship athletes are identical except for 28.7% of the athletes.
B) the maximum difference in GPAs between male and female scholarship athletes is 0.287.
C) the chance that a pair of randomly chosen male and female scholarship athletes would have a significant difference in GPAs is 0.287.
D) the chance of obtaining a difference in GPAs between male and female scholarship athletes as large as that observed in the sample if there is no actual difference in mean GPAs is 0.287.