Deck 23: Hypothesis Testingexamples and Case Studies

Question 1

Suppose you are conducting a one-sided hypothesis test for a difference in two means (using 2 independent large samples), and you have a test statistic of −2.3, which is in the direction of the alternative hypothesis.How extreme is this value and what is your conclusion for this test?

Answer 1

The p-value is .01, which is pretty extreme.conclusion: reject the null hypothesis because the p-value is < .05.There is a significant difference between the two population means, and the first population has a smaller mean than the second.

Question 2

If the null and alternative hypotheses can be expressed in terms of a population proportion or mean, and if the sample sizes are large, then the test statistic is simply the _______________ associated with the sample proportion or sample mean (assuming the null hypothesis is true).

Answer 2

standardized score

Question 3

Suppose you are told that "no relationship was found between two variables" or that "no difference was found between two groups." What does the researcher really mean, in terms of a hypothesis test?

Answer 3

the results are not statistically significant.Chance has not been ruled out as an explanation.

Question 4

For Questions , use the following narrative
Narrative: Math pass
"Higher math exam pass rates were observed in the group who got 10 hours of tutoring per week compared to those who didn't (87% versus 77%) (p<.05)."
{Math pass narrative} Explain why it would have been better if they had reported the actual p-value.

Question 5

For Questions , use the following narrative
Narrative: Math pass
"Higher math exam pass rates were observed in the group who got 10 hours of tutoring per week compared to those who didn't (87% versus 77%) (p<.05)."
{Math pass narrative} What significance level is implied by the way the results are presented?

Question 6

Suppose you are conducting a one-sided hypothesis test for a difference in two means (using 2 independent large samples), and you have a test statistic of +2.3, which is in the direction of the alternative hypothesis.How extreme is this value and what is your conclusion for this test?

Question 7

Even when information in a news article is sparse, you can sometimes piece the information together to figure out certain parts of the hypothesis test on your own.What piece of information is not possible to figure out unless it is given to you?

A)The p-value or the test statistic.
B)The null and alternative hypotheses.
C)The impact of the conclusions.
D)All of the above.

Question 8

Journal articles very often report the p-value for their results, rather than just stating their conclusions as to whether or not they found a statistically significant result.Explain why this is important to you as an educated consumer of statistical information.

Question 9

Why is it important to remember the four steps of a hypothesis test?

A)So you can use them as a guideline to evaluate studies based on hypothesis tests.
B)So you know what questions to ask when you are just presented with a sound byte talking about a "statistically significant result."
C)Knowing what should be occurring behind the scenes helps you translate what you read, see, and hear, into a bigger picture.
D)All of the above.

Question 10

When you read the results of hypothesis tests in a newspaper, you are given very little information about the details of the test.What is often missing (name two things)?

Question 11

Suppose the p-value for your hypothesis test for a difference of two means was .001.Which of the following is an appropriate conclusion?

A)You reject the null hypothesis.
B)If there really was no difference in the population means, we would see results as extreme as these only .1% of the time.
C)You conclude that there is a statistically significant difference between the population means.
D)All of the above.

Question 12

Suppose you suspect that a majority of the people in your neighborhood would like to start a neighborhood watch program, but you want to conduct a hypothesis test to find out.What are your null and alternative hypotheses? Use symbols and numbers, and explain your symbols in words.

Question 13

What do we call a hypothesis test when the alternative hypothesis includes a possible difference in either direction?

A)A two-direction test.
B)A two-sided test.
C)A test that is not possible to conduct.
D)None of the above.

Question 14

Suppose you are told that "a relationship has been found between two variables" or that "a difference has been found between two groups." What does the researcher really mean, in terms of a hypothesis test?

Question 15

The _______________ is the standardized score for the sample value when the null hypothesis is true.

Question 16

For Questions , use the following narrative
Narrative: Math pass
"Higher math exam pass rates were observed in the group who got 10 hours of tutoring per week compared to those who didn't (87% versus 77%) (p<.05)."
{Math pass narrative} Explain what these results mean in terms a non-statistics student would understand.

Question 17

What is the relationship between the standard score and the p-value for a hypothesis test?

Question 18

For Questions , use the following narrative
Narrative: Math pass
"Higher math exam pass rates were observed in the group who got 10 hours of tutoring per week compared to those who didn't (87% versus 77%) (p<.05)."
{Math pass narrative} Name one issue that you would have to look into before you treat these results as credible.

Question 19

Suppose your test statistic for a two-sided test for the difference in two means resulted in a standard score of 0.What would the resulting p-value be?

A)0
B).5
C)1
D)Not enough information to tell.

Question 20

Why is it preferable to choose a one-sided alternative rather than a two-sided alternative in the situation where you are only interested in results that are extreme in one direction?

A)Your p-value would be half as much as it would be for a two-sided test (assuming the test statistic is the same each time, and is in the direction of the one-sided alternative you selected.)
B)Your results don't have to be as extreme in order to achieve statistical significance.
C)Your conclusions can be more informative because they will have a direction associated with them.
D)All of the above.

Question 21

Even if researchers used an extremely sophisticated statistical analysis from a complicated hypothesis test and study, there is one piece of information that you'll always be able to interpret and understand.What is that piece of information?

A)The p-value.
B)The test statistic.
C)The design of the study/experiment.
D)None of the above.

Question 22

A p-value is calculated under the assumption that the null hypothesis is __________.

Question 23

What does a p-value from a hypothesis test not tell you?

A)The direction of the difference or relationship (if one exists).
B)How extreme the observed difference or relationship was.
C)Whether or not your results are statistically significant.
D)How likely it is to have observed these particular results (or more extreme ones) given that the null hypothesis is true.

Question 24

The p-value __________ (choose: is, is not) equal to the probability that the null hypothesis is true.

Question 25

Suppose you are examining the difference between two means, and you conduct a two-sided hypothesis test and your friend constructs a confidence interval.Assuming that both reveal that the null hypothesis should be rejected, what can the confidence interval tell you that the hypothesis test cannot?

A)The magnitude of the difference in the means.
B)The direction of the difference in the means.
C)How much variability there was in the observed results.
D)All of the above.