A number of Mason faculty, staff, and students commute to campus using a bike. A researcher was interested in discovering if a difference exists between an individual bike frame material and the time it takes to get to campus. In particular, the two types of bikes the researcher focused on were carbon-framed and steel-framed bikes. A random sample of bikers using a carbon-framed bike and another random sample of bikers using a steel-framed bike was selected and their time to Mason in minutes from a distance three miles away was recorded (we will subtract Carbon - Steel). You may assume all conditions that allow for inference using a t-distribution are met. The data set is called "Type of Bike 1." Use the significance level = 0.05.

a) Define the population parameter in the context of this question in one sentence.

b) State the hypotheses you would use to test the claim that a difference exists in the mean time to Mason from the distance of three miles away for carbon-framed and steel-framed bikes.

c) compute the test statistic and p-value.

d) Based on the p-value from the output produced in part (c), state the decision you would make in this hypothesis test. Write your answer in one sentence and provide a reason for this decision.

e) State your conclusion in the context of this hypothesis test. Write your answer in context in one or two sentences.

f) Construct the 95% confidence interval in StatCrunch

g) Does the 95% confidence interval contain 0? Answer this question in one sentence.

h) Explain how your answer to part (g) connects to the decision you make in part (d) in one sentence.

i) Provide at least one confounding variable that may have had an effect on this study's results in one sentence.

PLEASE USE THE DATA SET BELOW

Carbon Steel 21.2 18.2 21.6 16.9 15.8 20.4 17.5 22.6 16.2 15.8 10.4 13.8 16.1 18.4 20.8 17.9 21.2 23.9 20.8 13.1 20.5 11.1 19.8 21.9 22.6 27.9 14.6 21.8 18.4 23.5 10.1 21.2 17.3 16.3 21 18.1 23.4 20.4 16.3 15.4 12.3 17.2 14.9 17.5 15.4 17.6 25.8 29.9 18.3 19.5 19.1 26.2 29.2 19.4 31.8 30.1 21.5 26.1