Deck 22: Rejecting Chancetesting Hypotheses in Research

Question 1

Which of the following is true about a p-value?

A)It measures the probability that the null hypothesis is true.
B)It measures the chance of observing your exact test statistic, assuming the null hypothesis were true.
C)It measures how likely you would be to observe results at or beyond your test statistic, assuming the null hypothesis is true.
D)All of the above.

Answer 1

It measures how likely you would be to observe results at or beyond your test statistic, assuming the null hypothesis is true.

Question 2

What numerical value do you calculate that gives you the answer to the question of how unlikely the test statistic would be if the null hypothesis were true?

Answer 2

the p-value

Question 3

Suppose a confidence interval for the difference in mean weight loss for two different weight loss programs (Program 1 - Program 2) is entirely above zero.What does this mean?

A)We can't say with any confidence that there is a difference in mean weight loss for the populations of people on these two programs.
B)We can say with confidence that there is a difference in mean weight loss for the populations of people on these two programs; further, we can say that the average weight loss on Program 1 is higher.
C)We can say with confidence that there is a difference in mean weight loss for the populations of people on these two programs; further, we can say that the average weight loss on Program 2 is higher.
D)None of the above.

Answer 3

We can say with confidence that there is a difference in mean weight loss for the populations of people on these two programs; further, we can say that the average weight loss on Program 1 is higher.

Question 4

For Questions , use the following narrative
Narrative: Cell phone survey
Suppose you suspect that most people are unhappy with their cell phone plans.You conduct a survey of 400 randomly selected cell phone owners ask them whether or not they are happy with their phone plans.Suppose 55% of the sample say no.
{Cell phone survey narrative} Suppose there is no clear opinion on how people perceive their cell phone plans (that is, 50% are happy with them, and 50% are not.) What is a reasonable range for the proportion of unhappy customers from numerous repeated samples of size 400 from this population?

Question 5

Which of the following conclusions do you draw if the p-value is not small enough to convincingly rule out chance?

A)We cannot reject the null hypothesis.
B)We accept the null hypothesis.
C)We are convinced that chance alone produced the observed results.
D)We accept the alternative hypothesis.

Question 6

The only way to conclude that the alternative hypothesis is the likely one is to have enough evidence to rule out __________, as presented in the __________ hypothesis.

Question 7

For Questions , use the following narrative
Narrative: Cell phone survey
Suppose you suspect that most people are unhappy with their cell phone plans.You conduct a survey of 400 randomly selected cell phone owners ask them whether or not they are happy with their phone plans.Suppose 55% of the sample say no.
{Cell phone survey narrative} What do you conclude, based on your survey results?

Question 8

For Questions , use the following narrative
Narrative: Cell phone survey
Suppose you suspect that most people are unhappy with their cell phone plans.You conduct a survey of 400 randomly selected cell phone owners ask them whether or not they are happy with their phone plans.Suppose 55% of the sample say no.
{Cell phone survey narrative} Suppose there is no clear opinion on how people perceive their cell phone plans (that is, 50% are happy with them, and 50% are not.) How likely would a value as large as .55 (or larger) be as the sample proportion in a sample of size 400?

Question 9

Suppose you have observed a sample mean and you want to know how likely it is that you would observe these results by chance given nothing interesting was going on in the population regarding its mean.Which of the following would help you determine that?

A)Find the standard score corresponding to your sample mean and interpret it.
B)Find the percentage of time you would expect to see results at least this large, in the case where there is nothing interesting happening in the population.
C)Find the range of reasonable values for sample means of this size, given nothing interesting is going on in the population, and see if your sample mean is in that range or not.
D)All of the above.

Question 10

When a relationship or value from a sample is so strong that we decide to rule out chance as an explanation for its magnitude, what does this mean?

A)The observed result is statistically significant.
B)We conclude that the observed result carries over to the population, and cannot be explained away by chance.
C)We could have been unlucky with our sample, and come to the wrong conclusion, but that chance is small.
D)All of the above.

Question 11

In the American judicial system, you must presume that the defendant is innocent unless there is enough evidence to conclude that he/she is guilty.What are the null and alternative hypotheses in this situation? Be sure to label which one is which.

Question 12

Is there a way to determine the probability that the null hypothesis is true? If yes, explain how; if no, explain why not.

Question 13

When a relationship or value from a sample is so strong that we can effectively rule out chance as an explanation, we say that the result is _______________.

Question 14

If there is nothing new happening in the population, in the long run you should expect __________ of the sample means from samples of size n taken from this population to be at or below the population mean, regardless of the standard deviation or the sample size.

Question 15

Once the hypotheses are set up, and the data have been collected and summarized in a test statistic, what is the next step, that ultimately leads you to make your decision?

Question 16

Which of the following conclusions do you draw if the p-value is small enough to convincingly rule out chance?

A)We reject the null hypothesis.
B)We accept the alternative hypothesis.
C)Our results are statistically significant.
D)All of the above.

Question 17

For Questions , use the following narrative
Narrative: Cell phone survey
Suppose you suspect that most people are unhappy with their cell phone plans.You conduct a survey of 400 randomly selected cell phone owners ask them whether or not they are happy with their phone plans.Suppose 55% of the sample say no.
{Cell phone survey narrative} A majority of the sample are unhappy with their cell phone plans.Does this automatically mean that a majority of the population of all cell phone owners are too? Explain why or why not (no calculations, please!)

Question 18

In general, the decision in a hypothesis test is based on a single summary of the data.What is this summary called?

A)The test score.
B)The sample mean.
C)The test statistic.
D)None of the above.

Question 19

Suppose the jury determines that the evidence presented by the prosecutors does not prove beyond a reasonable doubt that the defendant is guilty.What is the difference between concluding that the defendant is innocent, and concluding that the defendant is not guilty (if any)?

Question 20

When researchers conduct a hypothesis test, what general question is being asked and answered regarding the sample versus the population?

Question 21

The hypothesis that motivates most studies and is usually the reason the data are being collected in the first place is the __________ hypothesis.

Question 22

Which of the following describes the power of a test?

A)It is the probability of making the correct decision when the alternative hypothesis is true.
B)Bigger samples result in more power for the test, and smaller samples result in less power for the test.
C)It is higher when the population value is farther from the value in the null hypothesis.
D)All of the above.

Question 23

Which of the following statements is true regarding the relationship between a Type I and Type II error in a given situation?

A)Their probabilities add up to 1.
B)A Type II error is two times as large as its corresponding Type I error.
C)As the probability of one of them increases, the probability of the other one decreases.
D)All of the above.

Question 24

What should you conclude if your p-value is greater than the level of significance?

A)Do not reject the null hypothesis.
B)Accept the null hypothesis.
C)Conclude that chance alone produced the observed results.
D)Accept the alternative hypothesis.

Question 25

For Questions , use the following narrative
Narrative: Coupons
Suppose you think that the proportion of coupon users in grocery stores in your town has decreased from 10 years ago.You know from previous research that 10 years ago, 35% of grocery store customers in your town used coupons.Suppose you take a random sample of 100 customers from a variety of grocery stores in your town, and you find that 25 percent of them use coupons.
{Coupons narrative} Write down the null and alternative hypotheses.

Question 26

Which of the following refers to the significance level of a test?

A)The p-value.
B)The chance of obtaining sample results at least as extreme as those you observed, when nothing is going on in the population.
C)A preset borderline value to compare with the p-value, in order to make a decision about whether or not to reject the null hypothesis.
D)None of the above.

Question 27

Suppose your hypothesis test results in the conclusion that the true population value is significantly different from what was given in the null hypothesis.Your next question might be, can I get some idea of what the true population value is? You can compute a _______________ based on your sample results to help you answer that question.

Question 28

For Questions , use the following narrative
Narrative: Coupons
Suppose you think that the proportion of coupon users in grocery stores in your town has decreased from 10 years ago.You know from previous research that 10 years ago, 35% of grocery store customers in your town used coupons.Suppose you take a random sample of 100 customers from a variety of grocery stores in your town, and you find that 25 percent of them use coupons.
{Coupons narrative} What is your conclusion? Please use words that a non-statistics student would understand, and justify your answer.Assume a significance level of .05.

Question 29

If only those values above the null hypothesis or only those values below the null hypothesis are listed in the alternative hypothesis, the test is called a __________ test.

Question 30

For Questions use the following narrative
Narrative: Disease testing
In terms of testing people for a disease, the medical community usually assumes you don't have the disease until it is proven that you do have it.
{Disease testing narrative} In this case, what would a type II error represent: a false positive test result or a false negative test result?

Question 31

For Questions use the following narrative
Narrative: Disease testing
In terms of testing people for a disease, the medical community usually assumes you don't have the disease until it is proven that you do have it.
{Disease testing narrative} In this case, what would a type I error represent: a false positive test result or a false negative test result?

Question 32

For Questions use the following narrative
Narrative: Disease testing
In terms of testing people for a disease, the medical community usually assumes you don't have the disease until it is proven that you do have it.
{Disease testing narrative} Which error would you rather be protected more against, a Type I or a Type II error, in this case? Explain.

Question 33

Suppose a two-sided hypothesis test for a population mean resulted in a p-value of 1.What would you conclude?

A)The sample mean is exactly equal to the value stated in the null hypothesis.
B)The test statistic is zero.
C)You cannot reject the null hypothesis.
D)All of the above.

Question 34

For Questions , use the following narrative
Narrative: Coupons
Suppose you think that the proportion of coupon users in grocery stores in your town has decreased from 10 years ago.You know from previous research that 10 years ago, 35% of grocery store customers in your town used coupons.Suppose you take a random sample of 100 customers from a variety of grocery stores in your town, and you find that 25 percent of them use coupons.
{Coupons narrative} Explain whether this is a one-sided or a two-sided test, and why.

Question 35

For Questions , use the following narrative
Narrative: Coupons
Suppose you think that the proportion of coupon users in grocery stores in your town has decreased from 10 years ago.You know from previous research that 10 years ago, 35% of grocery store customers in your town used coupons.Suppose you take a random sample of 100 customers from a variety of grocery stores in your town, and you find that 25 percent of them use coupons.
{Coupons narrative} What is the value of the test statistic for your observed results?

Question 36

Which of the following is true when a Type I error has been committed?

A)The null hypothesis has to have been true.
B)The data must have convinced us that the alternative hypothesis was true.
C)The probability of making a Type I error is equal to the stated level of significance, usually .05.
D)All of the above.

Question 37

For Questions , use the following narrative
Narrative: Coupons
Suppose you think that the proportion of coupon users in grocery stores in your town has decreased from 10 years ago.You know from previous research that 10 years ago, 35% of grocery store customers in your town used coupons.Suppose you take a random sample of 100 customers from a variety of grocery stores in your town, and you find that 25 percent of them use coupons.
{Coupons narrative} What is the p-value for your observed results?

Question 38

Which of the following conclusions do you draw if the p-value is smaller than the level of significance?

A)Reject the null hypothesis.
B)Accept the alternative hypothesis.
C)The true population value is significantly different from the value in the null hypothesis.
D)All of the above.

Question 39

Explain in words what two errors you can make when drawing conclusions from a hypothesis test.

Question 40

In the jury trial scenario, our null hypothesis is "innocent" and our alternative hypothesis is "guilty." Explain which of the two potential errors is more serious, and justify your answer.

Question 41

Making a Type I error is only possible if the __________ hypothesis is true.

Question 42

What is the relationship between the power of a test and the types of errors you can make?

A)The power of a test is equal to 1 minus the probability of a Type II error.
B)The power of a test is equal to the sum of the probabilities of a Type I and Type II error.
C)The power of a test is equal to 1 minus the probability of a Type I error.
D)There is no relationship between power and Type I or Type II errors.

Question 43

Making a Type II error is only possible if the __________ hypothesis is true.