2.5. Refer to Copier maintenance Problem 1.20. Estimate the change in the mean s

Question

2.5. Refer to Copier maintenance Problem 1.20. Estimate the change in the mean service time when the number of copiers serviced increases by one. Use a 90 percent confidence interval. Interpret your confidence interval a. b. Conduct a t test to determine whether or not there is a linear association between X and Y here; control the risk at .10. State the alternatives, decision rule, and conclusion. What is the P-value of your test? c. Are your results in parts (a) and (b) consistent? Explain. d. The manufacturer has suggested that the mean required time should not increase by more than 14 minutes for each additional copier that is serviced on a service call. Conduct a test to decide whether this standard is being satisfied by Tri-City. Control the risk of a Type I error at.05. State the alternatives, decision rule, and conclusion. What is the P-value of the test? e. Does bo give any relevant information here about the "start-up" time on calls i.e, about the time required before service work is begun on the copiers at a customer location?

Explanation / Answer

This is the problem of simple linear regression.
Model:Y = A+BX
where Y:total number of minutes spent by the service person
X:number of copies serviced
A:intercept
B:slope i.e. amount of change in the mean service time when the number of copiers serviced increses by one.
A)
Estimate of B:
We can estiamte by using method of least square and we get
Bhat = Sxy/Sxx where Sxy=sum(x-xbar)(y-ybar) and Sxx=sum(x-xbar)^2

Sxy=5118.66666666667 Sxx=80376.8
Bhat=0.063683385
Confidence interval:
Bhat ± tnm1,/2*SE=(0.06024363,0.06712314)
B)
t-test:
H0 : B = 0 Ha : B != 0
The test statistic: t =(Bhat0)/sd(Bhat)=0.002046/0.063683385=31.1258
pvalue=<2e-16
The decision rule: reject H0 if t > 1.681, or equivalently, reject H0 if the p-value< 0.1

Here t>1.681 so reject H0 i.e. there is association between X and Y
C)
The results from part a and part b are consistent. The 90% confidence interval of B does
not include 0, so we expect that the hypothesis that B = 0 at a 10% significance level will
be rejected.

Find relevant R code:

data=read.csv("E:/Chegg/data.csv")
dim(data)
names(data)
model=lm(Yi~Xi,data=data)
summary(model)
confint(model, 'Xi', level=0.90)

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