Question

Cars on Campus. Statistics students at a community college wonder whether the cars belonging to students are, on average, older than the cars belonging to faculty. They select a random sample of 11 cars in the student parking lot and find the average age to be 7.5 years with a standard deviation of 5.6 years. A random sample of 20 cars in the faculty parking lot have an average age of 4.2 years with a standard deviation of 4 years.

1. The null hypothesis is H0:μs=μfH0:μs=μf. What is the alternate hypothesis?
A. HA:μs>μfHA:μs>μf
B. HA:μs<μfHA:μs<μf
C. HA:μs≠μfHA:μs≠μf

2. Calculate the test statistic.  ? z t X^2 F  =

3. Calculate the p-value for this hypothesis test.
p value =

4. Suppose that students at a nearby university decide to replicate this test. Using the information from the community college, they calculate an effect size of 0.72. Next, they obtain samples from the university student and faculty lots and, using their new sample data, conduct the same hypothesis test. They calculate a p-value of 0.0149 and an effect size of 0.423. Do their results confirm or conflict with the results at the community college?
A. It can neither confirm or contradict the community college results because we don't know the sample sizes the university students used.
B. It contradicts the community college results because the p-value is much bigger
C. It confirms the community college results because the p-value is much smaller.
D. It confirms the community college results because the effect size is nearly the same.
E. It contradicts the community college results because the effect size is much smaller.

Answer 1

From the given data

1. The null hypothesis is H0:μs=μf. What is the alternate hypothesis?
Correct answer: Option (A). HA:μs>μf

2. Calculate the test statistic.  t = 1.905

3. Calculate the p-value for this hypothesis test.

p value = 0.0334

4. Suppose that students at a nearby university decide to replicate this test. Using the information from the community college, they calculate an effect size of 0.72. Next, they obtain samples from the university student and faculty lots and, using their new sample data, conduct the same hypothesis test. They calculate a p-value of 0.0149 and an effect size of 0.423. Do their results confirm or conflict with the results at the community college?

Correct answer: Option (E) It contradicts the community college results because the effect size is much smaller.