Statistical Inference Refresher!

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 for male & female athletes (P = 0.287). This means that...

• the GPAs for male and female scholarship athletes are identical, except for 28.7% of the athletes.
• the maximum difference in GPAs between male and female scholarship athletes is 0.287.
• the chance of obtaining a difference in GPAs between male and female scholarship athletes as large as that observed in the sample, if there is no difference in mean GPAs, is 0.287.
• the chance that a pair of randomly chosen male and female scholarship athletes would have a significant difference in GPAs is 0.287.

A researcher plans to conduct a test of hypotheses at the α = 0.01 significance level. She designs her study to have a power of 0.90 at a particular alternative value of the parameter of interest. The probability that the researcher will commit a Type I error is

• 0.01
• 0.10
• 0.89
• Cannot be determined

In testing hypotheses, if the consequences of incorrectly rejecting the null hypothesis are very serious, we should...

• use a very large level of significance.
• use a very small level of significance
• insist that the P-value be smaller than the level of significance.
• PANIC! And pretend you didn't get the experiment...

An advertiser wishes to see if a new advertisement is effective. The previous advertisement has a recognition score of 3.7. An SRS of 12 potential buyers resulted in a mean score of 3.4 with a st deviation of 1.7. Which of the following required conditions for conducting a t-test has not been met?

• The population is at least 10 times the sample size
• The data are taken from a simple random sample.
• The decision of each buyer is independent.
• The population is Normally distributed or n is large.

You are thinking of using a t-procedure to test hypotheses about the mean of a population using an alpha of 0.05. You suspect that the distribution of the population is NOT normal and may be moderately skewed. Which of the following statements is correct?

• You should not use the t procedure because the population does not have a normal distribution
• You may use the t procedure provided your sample size is at least thirty.
• You may use the t procedure, but you should probably claim only that the significance level is 0.10.
• You should be using z-test statistic and not the t-test statistic.

Tags

CCSS.HSS.IC.B.4

An engineer designs an improved light bulb. The previous design had an average life of 1200 hours. The new bulb had a lifetime of 1201 hours, using a sample of 2000 bulbs. Although the difference is quite small, the effect was statistically significant. The explanation is that...

• new designs have more variability than standard designs.
• the sample size is very large.
• the new bulbs last longer than the old bulb.
• All of the above.

Tags

CCSS.6.SP.A.3

“An uncontrolled experiment in 17 women found a significantly improved mean clinical symptom score after treatment. Methodologic flaws make it difficult to interpret the results of this study.” The authors of this paper are skeptical about the significant improvement because...

• there is no control group, so the improvement might be due to the placebo effect or to the fact that many medical conditions improve over time
• the response variable might not have an exactly Normal distribution in the population.
• the study didn’t use enough subjects to achieve any statistically significant findings.
• the P-value given was P = 0.03, which is too large to be convincing

Tags

CCSS.HSS.IC.B.3

An experiment to test the effectiveness of treatments with fluoride to reduce tooth decay involved 36 volunteers who had half of their teeth—the right or left side, determined by a coin—painted with a fluoride every six months for 5 years. At the end, the number of cavities during the treatment period was compared to the control. The appropriate test is...

• One-sample z-test of proportions
• One-sample t-test on paired data
• Two-sample t-test for difference of means
• Two-sample z-test for difference of means

Some scientists believe that a new drug would benefit about half of all people with a certain blood disorder. To estimate the proportion of patients who would benefit, the scientists will give it to a random sample of patients who have the disorder. What sample size is needed so that the 95% confidence interval will have a width of 0.06? 

• 748 
• 1,068
• 1,503
• 2,056 

Tags

CCSS.HSS.IC.B.4

With a sample size 18 and t=-3.56, should the null hypothesis be rejected in a two-sided test for a mean?

• yes if alpha is 0.05 and yes if alpha is 0.01
• yes if alpha is 0.05, but no if alpha is 0.01
• no of alpha is 0.05, but yes if alpha is 0.01
• never, because t is negative

Tags

CCSS.HSS.ID.A.4