Name that Test
Grab Bag
Interpretations
100
A scientist splits a group of 60 volunteers into two groups. One group takes a test while listening to classical music. The other takes the same test in silence. Each participant’s score out of 20 is measured.
two-sample t-test for the difference between means
100
What is the critical value for a 80% confidence interval of a population mean for a sample size of 15?
1.345
100
A mathematician calculates a confidence interval for a sample mean at a confidence level of 95% . What does the 95% mean in this context?
If she were to calculate the confidence interval using this method many, many times the confidence interval would capture the population mean about 95% of the time.
200
A teacher gives his entire class a pre-test for a topic. Two weeks later, after conducting several investigative activities with the class, he gives them the same test again.
matched pairs t-test for the mean difference
200
Mariah takes a sample of students at her school to see if they get the average amount of sleep for people their age. She does some research and finds that the average amount of sleep for high school teenagers is 7 hours and runs a test with these hypotheses. Calculate the test statistic for this test:
t = 1.626
200
Mariah takes a sample of students at her school to see if they get the average amount of sleep for people their age. She does some research and finds that the average amount of sleep for high school teenagers is 7 hours and runs a test with these hypotheses and results. What conclusions should be drawn from this test?
Since the p-value of 0.117 is larger than a reasonable significance level of 0.05, we fail to reject the null hypothesis. There is no evidence students are not getting an average of 7 hours of sleep.
300
A pollster polls 1248 people including 612 men and 636 women. One question asked is “Do you listen to country music?” The pollster wants to identify if there is a difference between men and women in this questions.
two-sample z-test for difference between proportions
300
Name this test:
A pollster asked, “What is your favorite kind of music?” with twelve different choices. She is interested to see if the answer to this question differs based on gender.
Chi-square test for independence
300
Mariah takes a sample of students at her school to see if they get the average amount of sleep for people their age. She does some research and finds that the average amount of sleep for high school teenagers is 7 hours and runs a test with these hypotheses and results. Interpret the p-value of this test:
The probability of this sample or something more extreme occurring is 11.7% if we assume the mean hours of sleep for teenagers is 7 hours.
400
A surplus hardware store sells large boxes full of screws of “assorted sizes” for low prices. A contractor wants to evaluate whether there are about the same number of each size screw in a box.
chi-square goodness of fit test
400
Mariah takes a sample of students at her school to see if they get the average amount of sleep for people their age. She does some research and finds that the average amount of sleep for high school teenagers is 7 hours. Calculate a confidence interval for the average amount of sleep for Mariah's school:
(6.992, 7.908)
400
It is hypothesized that a certain medical procedure (procedure A) has a faster recovery rate than the standard procedure (procedure B). An experiment is run to compare the average recovery time for the procedures at 0.05 significance level. Describe a type two error in this test:
A Type II error would mean that procedure A heals people faster on average, yet you failed to reject the null hypothesis that they were the same.
500
A commercial claims that replacing one meal a week with SlimQuick shakes helps overweight people lose “at least 10 lbs in a month!” on average. A doctor decides to conduct a study to test whether this claim applies to his patients.
one-sample t-test for the population mean
500
A statistician used a sample size of 200 to collect data to estimate a population parameter. What would happen to the confidence interval if she increased her sample size to 400 and changed nothing else? (Use numbers in your answer.)
The margin of error would decrease by a factor of
sqrt2 or about 1.414
500
A container of milk from a bottling plant is supposed to contain 3.78 L of milk. It is suspected that one of the bottling machines is under-filling the bottles. A random sample of 100 bottles is measured to see if the average fill amount is significantly different than 3.78 L. Describe a type I error in this test:
The null hypothesis was rejected, though the machine is filling the bottles at the correct level of 3.78 mL.