To handle this issue, she decided to pair by rider. She took one random sample of 17 riders and allowed each rider to use both a carbonframed bike and a steel-framed bike. In addition, on the day each individual was to ride, she flipped a coin to see which bike the rider would use on the first of the two rides. The same variable (time to Mason in minutes from a distance three miles away) was recorded for each rider using both types of bikes. We are still testing the claim that a difference exists in the mean time it takes to ride to Mason from the distance of three miles away for different bike frame types. The data set is called "Type of Bike 2" and we will use = 0.05 in this investigation.

a) Calculate the difference between the time to Mason using a carbon-framed and steelframed bike Please subtract (Cabon - Steel). List the difference for each of the pairs in one column in your solutions document.

b) Obtain the sample mean of these differences and the sample standard deviation of these

c) Define the population parameter in context in one sentence.

d) State the null and alternative hypotheses using correct notation.

e) Create a frequency histogram overlaid with a Normal curve of the sample differences and create a boxplot of the sample differences. Title and label each graph appropriately and copy these graphs into your solutions document.

f) Provide a one sentence comment about these graphs that allow us to continue conducting inference using the t-distribution in this problem.

g) Calculate the test statistic "by hand" and be sure to show your work (please type this work). Use the rounded values you obtained in part (b). Round the test statistic to three decimal places.

h) Calculate the p-value type the correct probability notation and the p-value rounded to four decimal places. In addition, state the degrees of freedom for this test and show how the degrees of freedom were calculated.

j) State your decision whether you reject or do not reject the null hypothesis and the reason for your decision in one sentence.

k) State your conclusion in context of the problem in one or two complete sentences.

PLEASE USE THE DATA SET BELOW

Rider	Carbon	Steel
1	15.7	18.9
2	21.7	23.5
3	18.3	21.1
4	13.7	15.9
5	15.8	15.9
6	23.9	26.3
7	21.2	20.8
8	23.8	21.8
9	14.7	18.9
10	18.9	21.5
11	15.7	16.9
12	27.8	29.7
13	19	19.9
14	19.4	19.2
15	20.3	24.8
16	22.2	22.7
17	17.1	19.7