Refer to Exercise 6.

(a) Interpret the value of SEb in context.

(b) Find the critical value for a 99% confidence interval for the slope of the true regression line. Then calculate the confidence interval. Show your work.

(c) Interpret the interval from part (b) in context.

(d) Explain the meaning of “99% confident” in context .

Given in the question that, We need to interpret the value of $S{E}_b$in context.

The researchers wanted to know how well the amount of beers a person drinks predicts his or her blood alcohol level. Sixteen individuals with a BAC of zero were given a random number of beer cans to drink. On the data, a least squares regression line was used. The question includes a residual plot and a residual histogram. For this data, the computer output is provided. The standard deviation of the slope is given in the row with "Perch" and the column with "Stdev.": $S{E}_b$

${\mathrm{SE}}_b=0.0024$

This suggests that the sample regression line's slope should differ by roughly $0.0024$from the population regression line's true slope.

Given in the question that, We need to find the critical value for a $99\%$ confidence interval for the slope of the true regression line. And calculate the confidence interval.

The researchers wanted to know how well the amount of beers a person drinks predicts his or her blood alcohol level. Sixteen individuals with a BAC of zero were given a random number of beer cans to drink. On the data, a least squares regression line was used. The question includes a residual plot and a residual histogram. For this data, the computer output is provided. As a result, it is stated,

$n=16$

$b=0.017964$

${\mathrm{SE}}_b=0.0024$

The sample size was reduced by two degrees of freedom:

$df=n-2$

$=16-2$

$=14$

In table B, the essential $\mathrm{t}$--value can be discovered in the row of $df=14$and the column of $c=99$percent as follows:

$t^{*}=2.977$

As a result, the confidence interval is as follows:

$b-t^{*}\times {\mathrm{SE}}_b$

$=0.017964-2.977\times 0.0024$

$=0.0108192$

$b+t^{*}\times {\mathrm{SE}}_b$

$=0.017964+2.977\times 0.0024$

$=0.0251088$

Given in the question that, We need to interpret the interval from part (b) in context.

The researchers wanted to know how well the amount of beers a person drinks predicts his or her blood alcohol level. Sixteen individuals with a BAC of zero were given a random number of beer cans to drink. On the data, a least squares regression line was used. The question includes a residual plot and a residual histogram. For this data, the computer output is provided. As a result, portion (b)

we have, $(0.0108192,0.0251088)$

As a result, we have a $99$percent confidence level that the true slope of the population regression line is between $(0.0108192,0.0251088)$.

Given in the question that, We need to explain the meaning of “$99\%$ confident” in context.

The researchers wanted to know how well the amount of beers a person drinks predicts his or her blood alcohol level. Sixteen individuals with a BAC of zero were given a random number of beer cans to drink. On the data, a least squares regression line was used. The question includes a residual plot and a residual histogram. For this data, the computer output is provided. In this case, "$99$percent confident" means that the confidence interval will contain the true value of the population parameter in$99$percent of all possible samples.