Exam 22: What Is a Test of Significance

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?

The null hypothesis is

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?

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

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 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 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 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?

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

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

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 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 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 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 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?

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

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:

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 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 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?