Resting pulse rate is an important measure of the fitness of a person's cardiovascular system, with a lower rate indicative of greater fitness. The mean pulse rate for all adult males is approximately 72 beats per minute. A random sample of 25 male students currently enrolled in the Agriculture School at a major university was selected and the mean resting pulse rate was found to be 80 beats per minute with a standard deviation of 20 beats per minute. The experimenter wishes to test if the students are less fit, on average, than the general population. The null and alternative hypotheses are:

H 0 : x-bar = 72; H a : x-bar < 72

H 0 : x-bar = 80; H a : x-bar > 72

Which of the following describes a Type II error in this setting?

Not concluding that the students are less fit (on average) as the general population when in fact they are less fit (on average).

Concluding that the students are less fit (on average) than the general population when in fact they have equal fitness on average.

Not concluding that the students are less fit (on average) as the general population when in fact they have the same fitness (on average).

Concluding that the students are less fit (on average) than the general population, when, in fact, they are less fit (on average).

Concluding that the students have the same fitness (on average) when in fact they are more fit (on average).

A group of nutritionists is hoping to prove that a new soybean compound has more protein per gram than roast beef, which has a mean protein content of 20. A random sample of 5 batches of the soy compound have been tested, producing protein contents of 15, 22, 17, 18, and 23. Which of the following conditions must be met in order to carry out a legitimate statistical test of the nutritionists’ claim?

The observations are from a Normally distributed population.

The data can be viewed as coming from a simple random sample.

The standard deviation of the population is known.

You collect test scores on four members of a population which you can safely assume is approximately Normally distributed and test the hypotheses H 0 : μ=100 versus H a : μ > 100. You obtain a P-value of 0.052. Which of the following statements is true?

There is some evidence against H 0 , and a study using a larger sample size may be worthwhile

At the 5% significance level, you have proved that H 0 is true.

You have failed to obtain any evidence for H a .

You can accept H a at the 5% significance level

You can accept H 0 at the 10% significance level.

Some people say that more babies are born in September than in any other month. To test this claim, you take a simple random sample of 150 students at your school and find that 21 of them were born in September. You are interested in whether the proportion born in September is higher than 1/12—what you would expect if September was no different from any other month. Thus your null hypothesis is H 0 : p= 1/12. The P-value for your test is 0.0056. Which of the following statements best describes what the P-value measures?

0.0056 is the probability of getting a sample with a proportion of September birthdays this far or farther above 1/12 if the true proportion is 1/12

The probability that September birthdays are no more common that any other month is 0.0056.

The probability that September birthdays are more common is 0.0056

The probability that the proportion of September birthdays in the population is not equal to 1/12 is 0.0056

0.0056 is the probability of getting a sample with a proportion of September birthdays this close to 1/12 if the true proportion is not 1/12

Looking online, you find the salaries of all 25 players for the Chicago Cubs as of opening day of the 2013 baseball season. The club total was $104 million, fourteenth in the major leagues. Which inference procedure would you use to estimate the average salary of the Cubs players?

None of these—this is not a situation that calls for inference

A medical experiment compared the herb Echinacea with a placebo for preventing colds. The study used 50 different response variables usually associated with colds, such as low-grade fever, congestion, frequency of coughing, etc. The subjects were 40 women between 25 and 40 years of age. At the end of the study, the Echinacea group displayed significantly better responses at the α = 0.05 level for three of the 50 response variables studied. Which of the following is an appropriate conclusion to draw from this study?

There is not sufficient evidence to conclude that Echinacea is beneficial. It is quite likely that the significant results for the three variables occurred by chance.

There is good evidence that Echinacea reduces cold symptoms.

There is good evidence that Echinacea reduces at least these three cold symptoms

There is good evidence that Echinacea reduces cold symptoms, but we should be careful not to extend our conclusions beyond women in this age group

There may be some benefits to Echinacea, but further study with a larger number of subject is necessary

A medical experiment compared the herb Echinacea with a placebo for preventing colds. The study used 50 different response variables usually associated with colds, such as low-grade fever, congestion, frequency of coughing, etc. The subjects were 40 women between 25 and 40 years of age. One response variable was “volume of nasal secretions” (if you have a cold, you blow your nose a lot). Take the average volume of nasal secretions in people without colds to be µ = 1. An increase to µ = 3 indicates a cold. Which of the following describes the significance level of a test of H 0 : µ=1 versus H a : µ>1?

The probability that the test rejects H 0 when µ = 1 is true

The probability that the test rejects H 0 when µ = 3 is true.

The probability that the test fails to reject H 0 when µ = 3 is true.

The probability that the test fails to reject H 0 when µ = 1 is true

Which one of the following actions will increase the power of a one-tailed t-test for a mean?

Decrease the level of significance

Increase the probability of a Type II error

Significance Tests Review Quiz

1.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

A significance test was performed to test the null hypothesis H₀ : p = 0.5 versus the alternative H_a: p > 0.5. The test statistic is z = 1.40. Which of the following is closest to the P-value for this test?

0.0808

0.1492

0.1616

0.2984

0.9192

2.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

The mean time it takes for a person to experience pain relief from aspirin is 25 minutes. A new ingredient is added to help speed up relief. Let µ denote the mean time to obtain pain relief with the new product. An experiment is conducted to verify if the new product works more quickly. What are the null and alternative hypotheses for the appropriate test of significance?

H0 : µ = 25 vs. Ha : µ ≠ 25

H0 : µ = 25 vs. Ha : µ < 25

H0 : µ < 25 vs. Ha : µ = 25

H0 : µ < 25 vs. Ha : µ > 25

H0 : µ = 25 vs. Ha : µ > 25

3.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

A test of H₀: µ=60 versus H_a: µ≠60 produces a sample mean of x-bar = 58 and a P-value of 0.04. At an α = 0.05 level, which of the following is an appropriate conclusion?

There is sufficient evidence to conclude that µ < 60.

There is sufficient evidence to conclude that µ = 60.

There is insufficient evidence to conclude that µ = 60.

There is insufficient evidence to conclude that µ ≠ 60

There is sufficient evidence to conclude that µ ≠ 60.

4.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Because t procedures are robust, the most important condition for their use is

the population standard deviation is known.

the population distribution is approximately Normal.

the data can be regarded as a random sample from the population.

np and n(1 – p) are both at least 10.

all values in the sample are within two standard deviations of the mean.

5.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

We want to test H₀: µ = 1.5 vs. H_a : µ ≠ 1.5 at α = 0.05 . A 95% confidence interval for µ calculated from a given random sample is (1.4, 3.6). Based on this finding we

fail to reject H₀

reject H₀

cannot make any decision at all because the value of the test statistic is not available

cannot make any decision at all because the distribution of the population is unknown

cannot make any decision at all because (1.4, 3.6) is only a 95% confidence interval for µ

6.

MULTIPLE SELECT QUESTION

2 mins • 1 pt

Which of the following statements is/are correct?

The power of a significance test depends on the effect size.

The probability of a Type II error is equal to the significance level of the test.

Error probabilities can be expressed only when a significance level has been specified.

7.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

The water diet requires you to drink two cups of water every half hour from the time you get up until you go to bed, but otherwise allows you to eat whatever you like. Four adult volunteers agree to test the diet. They are weighed prior to beginning the diet and after six weeks on the diet. The weights (in pounds) are (in photo). Which of the following conditions must be met in order to use a t-procedure on these paired data?

Only the distribution of pre-diet weights must be approximately Normal.

Only the distribution of differences (after 6 weeks – before) must be approximately Normal.

The distribution of both pre-diet weights and six-week weights must be approximately Normal.

The distribution of pre-diet weights and the distribution of differences (after 6 weeks – before)

must be approximately Normal.

All three distributions—before diet, after 6 weeks, and the difference—must be approximately Normal.

8.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

The water diet requires you to drink two cups of water every half hour from the time you get up until you go to bed, but otherwise allows you to eat whatever you like. Four adult volunteers agree to test the diet. They are weighed prior to beginning the diet and after six weeks on the diet. The weights (in pounds) are (see photo). What would a Type II error be for this test of the water diet?

Concluding that the diet leads to weight loss when it doesn’t.

Concluding that the diet leads to weight loss when it really does.

Not concluding that the diet leads to weight loss when it does.

Not concluding that the diet leads to weight loss when it really doesn’t.

Drawing a conclusion from this test when the Normality condition has not been satisfied.

9.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

A researcher wishes to determine if people are able to complete a certain pencil and paper maze more quickly while listening to classical music. Suppose previous research has established that the mean time needed for people to complete a certain maze (without music) is 40 seconds. The researcher, therefore, decides to test the hypotheses H₀: µ = 40 versus H_a: µ < 40 , where µ is the time in seconds needed to complete the maze while listening to classical music. To do so, the researcher has 10,000 people complete the maze with classical music playing. The mean time for these people is x-bar = 39.92 seconds, and the P-value of his significance test is 0.0002. Which statement below best describes the appropriate conclusion to draw from this study?

The researcher has proved that listening to classical music substantially improves the time it takes to complete the maze.

The researcher has strong evidence that listening to classical music substantially improves the time it takes to complete the maze.

The researcher has moderate evidence that listening to classical music substantially improves the time it takes to complete the maze.

Although the researcher has obtained a statistically significant result, it appears to have little practical significance.

Since the P-value is greater than the reciprocal of the sample size, this is not a significant result.

10.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

The recommended daily Calcium intake for women over 21 (and under 50) is 1000 mg per day. The health services at a college are concerned that women at the college get less Calcium than that, so they take a random sample of female students in order to test the hypotheses H₀: μ =1000 versus H_a: μ<1000. Prior to the study they estimate that the power of their test against the alternative H_a:μ=900 is 0.85. Which of the following is the best interpretation of this value?

The probability of making a Type II error.

The probability of rejecting the null hypothesis when the parameter value is 1000.

The probability of rejecting the null hypothesis when the parameter value is 900.

The probability of failing to reject the null hypothesis when the parameter value is 1000.

The probability of failing to reject the null hypothesis when the parameter value is 900.

Significance Tests Review

20 questions

A significance test was performed to test the null hypothesis H₀ : p = 0.5 versus the alternative H_a: p > 0.5. The test statistic is z = 1.40. Which of the following is closest to the P-value for this test?

A test of H₀: µ=60 versus H_a: µ≠60 produces a sample mean of x-bar = 58 and a P-value of 0.04. At an α = 0.05 level, which of the following is an appropriate conclusion?

Because t procedures are robust, the most important condition for their use is

We want to test H₀: µ = 1.5 vs. H_a : µ ≠ 1.5 at α = 0.05 . A 95% confidence interval for µ calculated from a given random sample is (1.4, 3.6). Based on this finding we

Which of the following statements is/are correct?

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Significance Tests Review

20 questions

A significance test was performed to test the null hypothesis H0 : p = 0.5 versus the alternative Ha: p > 0.5. The test statistic is z = 1.40. Which of the following is closest to the P-value for this test?

A test of H0: µ=60 versus Ha: µ≠60 produces a sample mean of x-bar = 58 and a P-value of 0.04. At an α = 0.05 level, which of the following is an appropriate conclusion?

Because t procedures are robust, the most important condition for their use is

We want to test H0: µ = 1.5 vs. Ha : µ ≠ 1.5 at α = 0.05 . A 95% confidence interval for µ calculated from a given random sample is (1.4, 3.6). Based on this finding we

Which of the following statements is/are correct?

Create a free account and access millions of resources

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

A significance test was performed to test the null hypothesis H₀ : p = 0.5 versus the alternative H_a: p > 0.5. The test statistic is z = 1.40. Which of the following is closest to the P-value for this test?

A test of H₀: µ=60 versus H_a: µ≠60 produces a sample mean of x-bar = 58 and a P-value of 0.04. At an α = 0.05 level, which of the following is an appropriate conclusion?

We want to test H₀: µ = 1.5 vs. H_a : µ ≠ 1.5 at α = 0.05 . A 95% confidence interval for µ calculated from a given random sample is (1.4, 3.6). Based on this finding we