The data in the accompanying table come from the

Chapter 11, Problem 101SE

(choose chapter or problem)

The data in the accompanying table come from the comparison of the growth rates for bacteria types A and B. The growth Y recorded at five equally spaced (and coded) points of time is shown in the table.

a Fit the linear model

            \(Y=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}+\beta_{3} x_{1} x_{2}+\varepsilon\)

to the n = 10 data points. Let x1 = 1 if the point refers to bacteria type B and let x1 = 0 if the point refers to type A. Let \(x_{2}\) = coded time.

b Plot the data points and graph the two growth lines. Notice that \(\beta_{3}) is the difference between the slopes of the two lines and represents time–bacteria interaction.

c Predict the growth of type A at time \(x_{2}=0\) and compare the answer with the graph. Repeat

the process for type B.

d Do the data present sufficient evidence to indicate a difference in the rates of growth for the two types of bacteria?

e Find a 90% confidence interval for the expected growth for type B at time x2 = 1.

f Find a 90% prediction interval for the growth Y of type B at time \(x_{2}=1).

Equation transcription:

Text transcription:

Y=beta{0}+beta{1} x{1}+beta{2} x{2}+beta{3} x{1} x{2}+varepsilon

X{2}

beta{3}

x{2}=0

x{2}=1