Given H0: μ = 25, Ha: μ ≠ 25, and P = 0.034. Do you reject or fail to reject H0 at the 0.01 level of significance?

not sufficient information to decide

In a random sample of 1000 adult Americans, only 430 could name at least one justice who is currently serving on the US Supreme Court. A claim is that fewer than half of adult Americans can name at least one justice who is currently serving on the US Supreme Court. State the null hypothesis.

H o :p =.5 where p is the true proportion of Americans who can name one justice currently serving.

H o : p <.5, where p is the true proportion of Americans who can name one justice currently serving.

H o :p >.5 where p is the true proportion of Americans who can name one justice currently serving.

In a random sample of 1000 adult Americans, only 430 could name at least one justice who is currently serving on the US Supreme Court. A claim is that fewer than half of adult Americans can name at least one justice who is currently serving on the US Supreme Court. State the alternative hypothesis.

H a : p<.5, where p is the true proportion of Americans who can name one justice currently serving.

H a : p=.5, where p is the true proportion of Americans who can name one justice currently serving.

H a : p>.5, where p is the true proportion of Americans who can name one justice currently serving.

In a national survey of 2013 adults, 1283 indicated that they believe rudeness is a more serious problem than in years past. Does this indicate that more than 3/4 of American adults believe rudeness is a worsening problem? State the null hypothesis.

H o : p = .75, where p is the true proportion of Americans who believe rudeness is worsening.

H o : p > .75, where p is the true proportion of Americans who believe rudeness is worsening.

H o : p < .75, where p is the true proportion of Americans who believe rudeness is worsening.

In a random sample of 1000 adult Americans, 700 indicated that they oppose the reinstatement of a military draft. Is there convincing evidence that the proportion of American adults who oppose the reinstatement of the draft is different from two-thirds? State the null hypothesis.

H o : p = 2/3, where p is the true proportion of American adults who oppose the reinstatement of the draft.

H o : p < 2/3, where p is the true proportion of American adults who oppose the reinstatement of the draft.

H o : p > 2/3, where p is the true proportion of American adults who oppose the reinstatement of the draft.

Sally reads a newspaper report claiming that 12% of all adults in the U.S. are left-handed. She decides to test this claim. Sally selects a random sample of 55 classmates and finds that 9 were left-handed. Does this provide sufficient evidence that the proportion of lefties in Sally’s school is different than the national figure? Use α = 0.01. Which is the correct conclusion for this test?

Snice p-value = 0.319 > 0.01, I fail to reject H0. There is not enough evidence to suggest a difference.

Snice p-value = 0.319 < 0.01, I reject H0. There is enough evidence to suggest a difference.

Snice p-value = 0.319 > 0.01, I reject H0. There is enough evidence to suggest a difference.

Snice p-value = 0.319 < 0.01, I fail to reject H0. There is enough evidence to suggest a difference.

A medical assistant sampled the blood pressures of 20 randomly selected patients with high blood pressure before and after they receive a dose of a new medicine. Which hypothesis test should she run?

Paired t-test. Since the patients are the same in both sample 1 and sample 2, the two samples are linked.

2-sample t-test. Since the blood pressures were taken for 20 patients in sample 1 and the same 20 patients in sample 2, use a two-sample t-test to see if the results are statistically significant.

1-sample t-test. The medical assistant should compare the mean of the first sample of 20 patients to the mean of the second sample of 20 patients.

2-sample t-test. There is no natural pairing between the two samples.

A researcher gave one group of people an active drug and gave a different group of people an inactive placebo, then compare the blood pressures between the groups. Which test should he run to determine the efficacy of the active drug?

2-sample t-test. Since the blood pressures were taken for patients in sample 1 and different patients in sample 2, use a two-sample t-test to see if the results are statistically significant.

Paired t-test. Since there is a group with the active drug and another with the inactive drug, he may pair the two two groups if the sample sizes are the same.

1-sample t-test. The researcher should compare the mean of the first sample of patients to the mean of the second sample of patients.

2-sample z-test. There is no natural pairing between the two samples, so the researcher must use a proportions test.

Is the mean height of female college students greater than 5.5 feet?

1-sample t-test. Test whether the mean of a single sample is equal to the target value of 5.5 feet.

Paired t-test. Students heights can be measured against females of similar backgrounds.

2-sample t-test. Test whether the heights of female college students is higher than their high school heights.

Use a z-test by finding the mean height and standard deviation of the sample of college females' heights.

Does the mean height of female college students significantly differ from the mean height of male college students?

2-sample t-test. Test whether the mean height of female college students is different than the mean height of male college students.

Paired t-test. Test whether the difference of the means of one male paired with one female is equal to 0.

1-sample t-test. Test whether the mean of randomly assigned pairs of female and male students is greater than the mean of the average of males and females.

z-test. Use proportions in place of means to run a one sample z-test for males and females and compare averages.

The fire department of a small city wants to know if the proportion of homes having at least one smoke detector is still 90%. They take a sample of 100 homes and check if they have working smoke detectors.

1-sample z-test. Since this is a proportion so we should use a z-test to see if the homes sampled still equal the current rate of 90% in this city.

Paired t-test. The homes surveyed can be compared with the 90% and determined if the difference in the homes with smoke detectors now is equal to zero.

1-sample t-test. This is a single sample of the mean estimated number of homes having smoke detectors.

2-sample t-test. Since the population value before was 90%, compare this to the current population and determine if the difference is 0 between before and now.

I run a paired t-test for 15 sets of first grade twins reading abilities if one twin used a computer program tutor and the other did not, and get a p-value of 0.02, what does this mean for a significance level of 0.05?

Reject the null hypothesis. There is evidence at the 0.05 level that the computer program tutor is more effective at raising reading scores.

Fail to reject the null hypothesis. There is no evidence at the 0.05 level that the computer program tutor is more effective at raising reading scores.

Accept the null hypothesis. There is evidence at the 0.05 level that the computer program tutor is more effective at raising reading scores.

This was not the proper use of a paired t-test; no conclusions can be drawn from this test.

Is there evidence that income levels are not evenly distributed across the entire population? What is the p value and chi square statistic?

yes, p value is 0, chi square statistic = 92.11

yes, p value is .242, chi square statistic = 43.98

no, p value is 0, chi square statistic = 92.11

no, p value is 2.42, chi square statistic = 43.98

Hypothesis Tests - Take Home Test

Authored by Kristen Joyal

Mathematics

12th Grade

CCSS covered

Used 22+ times

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MULTIPLE CHOICE QUESTION

1 min • 1 pt

A P-value indicates:

the probability that the null hypothesis is true

the probability that the alternative hypothesis is true

the probability of obtaining the results (or one more extreme) if the null hypothesis is true

probability of a Type I error

Which of the following represents the appropriate null & alternative hypotheses?
The mean height of women is greater than 64"

H₀: μ > 64"
Hₐ: μ ≠ 64"

H₀: μ = 64"
Hₐ: μ > 64"

H₀: p > 64"
Hₐ: p ≠ 64"

H₀: p = 64"
Hₐ: p > 64"

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Suppose the P-value for a hypothesis test is 0.0304. Using a = 0.05, what is the appropriate conclusion?

a) reject the null

b) reject the alternative

c) Accept the null

d) Fail to reject the alternative

MULTIPLE CHOICE QUESTION

1 min • 1 pt

In their advertisements, a new diet program would like to claim that their methods result in a mean weight loss of more than ten pounds in two weeks. In order to determine if this is a valid claim, they hire an independent testing agency that then selects twenty-five people to be placed on this diet. The agency should be testing the null hypothesis H₀: m = 10 and the alternative hypothesis

Ha: μ < 10

Ha: μ > 10

Ha: μ ≥ 10

Ha: μ ≤ 10

When p-value is greater than alpha we:

Reject Ho

Accept Ha

Accept Ho

Reject Ho

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Which of the following represents the appropriate null & alternative hypotheses?
The mean height of women is greater than 64"

H₀: μ > 64"
Hₐ: μ ≠ 64"

H₀: μ = 64"
Hₐ: μ > 64"

H₀: p > 64"
Hₐ: p ≠ 64"

H₀: p = 64"
Hₐ: p > 64"

Which of the following shows a right-tailed test?

H₁: µ < 15

H₀: µ < 15

H₁: µ > 15

H₀: µ > 15

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Hypothesis Tests - Take Home Test

A P-value indicates:

Which of the following represents the appropriate null & alternative hypotheses?The mean height of women is greater than 64"

Suppose the P-value for a hypothesis test is 0.0304. Using a = 0.05, what is the appropriate conclusion?

When p-value is greater than alpha we:

Which of the following represents the appropriate null & alternative hypotheses?The mean height of women is greater than 64"

Which of the following shows a right-tailed test?

A manufacturer claims that his tires last at least 40,000miles. A test on 25 tires reveals that the mean life of a tireis 39,750 miles, with a standard deviation of 387 miles.Test the Manufacturer’s claim at α = .01.

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Which of the following represents the appropriate null & alternative hypotheses?
The mean height of women is greater than 64"

Which of the following represents the appropriate null & alternative hypotheses?
The mean height of women is greater than 64"

A manufacturer claims that his tires last at least 40,000
miles. A test on 25 tires reveals that the mean life of a tire
is 39,750 miles, with a standard deviation of 387 miles.
Test the Manufacturer’s claim at α = .01.