Tests of Significance

1 / 10

The makers of Mini-Oats cereal have an automated packaging machine that is set to fill boxes with 24 ounces of cereal. At various times in the packaging process, a random sample of 100 boxes is taken to see if the machine is filling the boxes with an average of 24 ounces of cereal. Which of the following is a statement of the null hypothesis being tested?

The machine is filling the boxes with the proper amount of cereal.

The machine is not filling the boxes with the proper amount of cereal.

The machine is not putting enough cereal in the boxes.

2 / 10

A research article gives a p-value of .001 in the analysis section. Which definition of a p-value is the most accurate?

The probability that the observed outcome will occur again.

The probability of observing an outcome as extreme or more extreme than the one observed if the null hypothesis is true.

The value that an observed outcome must reach in order to be considered significant under the null hypothesis.

The probability that the null hypothesis is true.

3 / 10

If a researcher was hoping to show that the results of an experiment were statistically significant they would prefer:

A large p-value

A small p-value

p-values are not related to statistical significance

4 / 10

A researcher compares men and women on 100 different variables using a two sample t-test. He sets the level of significance to .05 and then carries out 100 independent t-tests (one for each variable) on these data. If, for each test, the null hypothesis actually is true, about how many "statistically significant" results will be produced?

0

5

10

None of the Above

5 / 10

Items 5 and 6 refer to the following situation:
Food inspectors inspect samples of food products to see if they are safe. This can be thought of as a hypothesis test where H0: the food is safe, and H1: the food is not safe. Identify each of the following statements as a Type I or a Type II error.

The inspector says the food is safe but it actually is not safe.

Type I

Type II

Not an error

6 / 10

The inspector says the food is not safe but it actually is safe.

Type I

Type II

Not an error

7 / 10

A newspaper article claims that the average age for people who receive food stamps is 40 years. You believe that the average age is less than that. You take a random sample of 100 people who receive food stamps, and find their average age to be 39.2 years. You find that this is significantly lower than the age of 40 stated in the article (p < .05). What would be an appropriate interpretation of this result?

The statistically significant result indicates that the majority of people who receive food stamps is younger than 40.

Although the result is statistically significant, the difference in age is not of practical importance.

An error must have been made. This difference is too small to be statistically significant.

8 / 10

A newspaper article stated that the US Supreme Court received 812 letters from around the country on the subject of whether to ban cameras from the courtroom. Of these 812 letters, 800 expressed the opinion that cameras should be banned. A statistics student was going to use this sample information to conduct a test of significance of whether more than 95% of all American adults feel that cameras should be banned from the courtroom. What would you tell this student?

This is a large enough sample to provide an accurate estimate of the American public's opinion on the issue.

The necessary conditions for a test of significance are not satisfied, so no statistical test should be performed.

With such a large number of people favoring the notion that cameras be banned, there is no need for a statistical test.

9 / 10

A researcher conducts an experiment on human memory and recruits 15 people to participate in her study. She performs the experiment and analyzes the results. She obtains a p-value of .17. Which of the following is a reasonable interpretation of her results?

This proves that her experimental treatment has no effect on memory.

There could be a treatment effect, but the sample size was too small to detect it.

She should reject the null hypothesis.

There is evidence of a small effect on memory by her experimental treatment.

10 / 10

It is reported that scores on a particular test of historical trivia given to high school students are approximately normally distributed with a mean of 85. Mrs. Rose believes that her 5 classes of high school seniors will score significantly better than the national average on this test. At the end of the semester, Mrs. Rose administers the historical trivia test to her students. The students score an average of 89 on this test. After conducting the appropriate statistical test, Mrs. Rose finds that the p-value is .0025. Which of the following is the best interpretation of the p-value?

A p-value of .0025 provides strong evidence that Mrs. Rose's class outperformed high school students across the nation.

A p-value of .0025 indicates that there is a very small chance that Mrs. Rose's class outperformed high school students across the nation.

A p-value of .0025 provides evidence that Mrs. Rose is an exceptional teacher who was able to prepare her students well for this national test.

None of the above.

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