Significance Testing

Multiple Choice

The weight of the average 6th grade student's backpack (with books in it) is 18.4 lbs. The principal of the school thinks that the backpack does not weight 18.4 lbs. What is the null and alternate hypothesis? 

• H₀ = 18.4 H_a = 18.4

• H₀ = 18.4 H_a > 18.4

• H₀ = 18.4 H_a < 18.4

• H₀ = 18.4 H_a ≠ 18.4

Multiple Choice

Which of the following is the FIRST step of a hypothesis test?

• Check assumptions & conditions

• Find your test statistic

• State your conclusion

• State your null & alternative hypotheses

Multiple Choice

A car manufacturer advertises that its new subcompact models get 47 mpg. If μ is the mileage of these cars, what could be the null and alternate hypothesis if we wanted to check if the car's mpg is overrated? 

• H₀ = 47 H_a = 47

• H₀ = 47 H_a < 47

• H₀ = 47 H_a > 47

• H₀ = 47 H_a ≠ 47

Multiple Choice

Identify the correct null hypothesis:

Is the proportion of babies born male different from 50%? In a sample of 200 babies, 96 were male. Test the claim using a level of significance of 1%.

• H₀: p = 0.50

• H₀: µ = 100

• H₀: p = 0.48

• H₀: µ = 96

Multiple Choice

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.

Multiple Choice

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.

Multiple Choice

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 alternative hypothesis.

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

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

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

Multiple Choice

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.

Multiple Choice

The Associated Press found that 730 of 1000 randomly selected adults preferred to watch movies at home rather than at a movie theater. Is there convincing evidence that the majority of adult Americans prefer watching movies at home? State the alternative hypothesis.

• H_a: p = .50, where p is the true proportion of adult Americans who prefer watching movies at home.

• H_a: p < .50, where p is the true proportion of adult Americans who prefer watching movies at home.

• H_a: p > .50, where p is the true proportion of adult Americans who prefer watching movies at home.

Multiple Choice

In a survey of 526 US businesses, 400 indicated that they monitor employee's web site visits. Is there sufficient evidence that more than 70% of US businesses monitor employees' web site visits? State the null hypothesis.

• H_o: p = .70, where p is the true proportion of US businesses that indicated they monitor employee web sites.

• H_o: p < .70, where p is the true proportion of US businesses that indicated they monitor employee web sites.

• H_o: p > .70, where p is the true proportion of US businesses that indicated they monitor employee web sites.

Multiple Choice

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.

Multiple Choice

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

• a) Reject the null hypothesis

• b) Reject the alternative hypothesis

• c) Fail to reject the null hypothesis

• d) Fail to reject the alternative hypothesis

Multiple Choice

When p-value is greater than alpha we:

• Reject Ho

• Fail to reject Ha

• Fail to reject Ho

• Reject Ha

Multiple Choice

In testing hypotheses, which of the following would be strong evidence against the null hypothesis?

• using a small level of significance

• using a large level of significance

• obtaining data with a small p-value

• obtaining data with a low test statistic

Multiple Choice

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

Multiple Choice

When performing a significance test, we're looking for convincing evidence to __________ the null hypothesis in favor of the alternative hypothesis.

• refute

• dispute

• reject

• accept

Multiple Choice

Small p-values mean that our sample was very unlikely if the null hypothesis is true. Therefore, small p-values are ________________ that the null hypothesis is wrong.

• convincing evidence

• believable proof

• reliable information

• justifiable inference

Multiple Choice

Whatever probability we choose as the cutoff for what is small is what we call the ____________________.

• importance level

• significance level

• meaningfulness level

• insightfulness level

Multiple Choice

The symbol for the significance level is ____.

• $$\alpha$$

• $$\theta$$

• $$\pi$$

• $$\mu$$

Multiple Choice

If p-value < $$\alpha$$  , then the sample is unusual if the null is correct, so we ______ the null and have convincing evidence that the alternative is true, and the results are ___________. 

• fail to reject, statistically significant

• reject, statistically significant

• fail to reject, not statistically significant

• reject, not statistically significant

Multiple Choice

If the p-value > $$\alpha$$  , then the sample is not unusual if the null is true, so we ______ the null, so there is not convincing evidence that the alternative hypothesis is true, so the results are ________. 

• fail to reject, not statistically significant

• fail to reject, statistically significant

• reject, not statistically significant

• reject, statistically significant

Multiple Choice

The drying supervisor uses the new method on a random sample of 200 boards.  She conducts a hypothesis test on her sample data and gets a p-value of .027. Based on the p-value , was there convincing evidence that the new method is better? Use  $$\alpha$$  = 0.05.

• Since our p-value of 0.027 is < $$\alpha$$  , we reject the null hypothesis. We have convincing evidence that the new method is better. 

• Since our p-value of 0.027 is >undefined , we fail to reject the null hypothesis. We do not have convincing evidence that the new method is better. 

Multiple Choice

At the end of the current growing season, the quality inspector took a sample of 50 pineapples and conducted a hypothesis test on the sample data. His test produced a p-value of 0.1317. Based on the p-value, was there convincing evidence that the current pineapples are larger? Use  $$\alpha$$  =0.05. 

• Since our p-value of 0.1317 is < $$\alpha$$  , we reject the null hypothesis. We have convincing evidence that the pineapples are larger. 

• Since our p-value of 0.1317 is >undefined , we fail to reject the null hypothesis. We do not have convincing evidence that the pineapples are larger. 

Multiple Choice

The label on bottles of one company's grapefruit juice say that they contain 180 ml of liquid. Your friend Jerry suspects that the true mean is less than that, so he takes a random sample of 40 bottles and measures the volume of liquid in each bottle. The mean volume of liquid in the bottles is 179.5 ml and the standard deviation is 1.3 ml. Jerry performs a test of Ho: $$\mu$$ = 180 ml versus Ha:< 180 ml. The test yields a p-value of 0.0098.  

Using a significance level of 1%, is there convincing evidence that there is less than 180 ml of liquid in the bottles? 

• Since our p-value of 0.0098 is more than $$\alpha$$ , we reject the null hypothesis. We have convincing evidence that the bottles contain less than 180 ml of liquid. 

• Since our p-value of 0.0098 is less thanundefined, we reject the null hypothesis. We have convincing evidence that the bottles contain less than 180 ml of liquid. 

• Since our p-value of 0.0098 is less thanundefined, we fail to reject the null hypothesis. We have convincing evidence that the bottles contain less than 180 ml of liquid. 

• Since our p-value of 0.0098 is more thanundefined, we fail to reject the null hypothesis. We have convincing evidence that the bottles contain less than 180 ml of liquid. 

Multiple Choice

The EPA has determined that safe drinking water should contain no more than 1.3 mg/L of copper, on average. To test water from a new source, you collect water in small bottles at each of 30 randomly selected locations/ The mean copper content of your bottles is 1.36 mg/L. You perform a test of Ho: $$\mu$$ = 1.3 mg/L versus Ha:>1.3 mg/L. 

The test yields a p-value pf 0.0391. What conclusion would you make for a significance level of 5%? 

• Since our p-value of 0.0391 is more than 5%, we reject the null hypothesis.  We have convincing evidence that the mean copper content of your bottles is greater than 1.3 mg/l.

• Since our p-value of 0.0391 is more than 5%, we fail to reject the null hypothesis.  We do not have convincing evidence that the mean copper content of your bottles is greater than 1.3 mg/l.

• Since our p-value of 0.0391 is less than 5%, we reject the null hypothesis.  We have convincing evidence that the mean copper content of your bottles is greater than 1.3 mg/l.

• Since our p-value of 0.0391 is less than 5%, we fail to reject the null hypothesis.  We do not have convincing evidence that the mean copper content of your bottles is greater than 1.3 mg/l.

Multiple Choice

Define a Type I error?

• The failure to reject a false null hypothesis

• Rejecting a true null hypothesis

• The acceptance to reject a null hypothesis

• Accepting a true null  hypothesis

Multiple Choice

A __________ occurs if you accept the null hypothesis when it is false.

• Type I error

• Type II error

Multiple Choice

A __________ occurs if you reject the null hypothesis when it is true.

• Type I error

• Type II error

Multiple Choice

Which of the following refers to a type I error?

• When a researcher wrongly accepts the results as being significant.

• When a researcher wrongly accepts the results as not being significant.

Multiple Choice

Which of the following refers to a type II error?

• When a researcher wrongly accepts the results as being significant.

• When a researcher wrongly accepts the results as not being significant.

Multiple Choice

A type I error involves a researcher wrongly accepting which hypothesis?

• Alternative

• Null

Multiple Choice

A type I error involves a researcher wrongly rejecting which hypothesis?

• Alternative

• Null

Multiple Choice

A type II error involves a researcher wrongly accepting which hypothesis?

• Alternative

• Null

Multiple Choice

A type I error involves a researcher wrongly rejecting which hypothesis?

• Alternative

• Null