A substance used in biological and medical research is shipped by airfreight to users in cartons of 1000 ampules.The data below, involving 8 shipments, were collected on the number of times the carton was transferred (X) from one aircraft to another over the shipment route and the number of ampules found to be broken upon arrival (Y).

x y

1 16

0 9

2 17

3 22

0 8

1 15

2 19

0 11

(a)Plot the points on a scatter diagram.Does there appear to be a linear trend?Estimate the least-squares regression line.

(b)Estimate the average number of broken ampules for 2 transfers.

(c)Construct a 95% confidence interval forb₁.Interpret the interval.

(d)Construct a 95% confidence interval and a 95% prediction interval for the mean value ofyusing anxvalue of 2.Explain the difference between these two intervals.

(e)Test for significance of regression using the two-sided t-test anda= 0.05.

(f)Construct an analysis of variance table and use it to perform the hypothesis test of part (e).Restate the null and alternative hypotheses and interpret your results.

(g)Calculate and interpret the sample coefficient of determination and the sample coefficient of correlation.

(h)Conduct a lack-of-fit test on the data.

(i)Perform a residual analysis on the data.

(j)Summarize your analysis of parts (a)-(i) in paragraph form and state the appropriateness of the model.

Picture 1: Hand Gripper The experiment consisted of: 1. Holding the hand gripper for a period of 10 seconds while standing up with their arm bent at a 90-degree angle 2. Gripping the power tool or pressure washer gun in the same way and pressing the trigger 5 tirnes 3. Gripping the Dynamometer in the same way and trying to exert the same amount of force as they did while pressing the trigger in either the power tool or the pressure washer 4. Two measurements of the force were recorded for each trial 5. Steps 1 to 4 were repeated for all trials with the variation of increasing the period of time the subject held the hand gripper to 20, 30, 40, 50, 60, 70, 80, 90, and 100 seconds (listed as Introduced Fatigue in data). We will focus on the measurements for one of the male candidates: \" Fati_ue (sec),X Force (Ll- , Y -E_ -_ \" -_ _ \" \" Perform a complete regression analysis using Minitab to determine whether or not the simple linear regression model is appropriate for this data. You m include a well written and m analysis in addition to the Minitab output. For any tests, use a = 0.05. Attach your Minitab output when handing in your assignment