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Chapter 12: Q. 11 (page 789)

Less mess? Kerry and Danielle wanted to investigate if tapping on a can of soda would reduce the amount of soda expelled after the can has been shaken. For their experiment, they vigorously shook 40cans of soda and randomly assigned each can to be tapped for 0seconds, 4seconds, 8seconds, or 12seconds. After opening the cans and waiting for the fizzing to stop, they measured the amount expelled (in milliliters) by subtracting the amount remaining from the original amount in the can. Here are their data:

Here is some computer output from a least-squares regression analysis of these data. Construct and interpret a 95%confidence interval for the slope of the true regression line.

Short Answer

Expert verified

The slope of the regression line is 95 percent certain to be between -2.9962298and -2.2737702.

Step by step solution

01

Given information

We have to construct and interpret the 95%confidence interval for the slope of the true regression line.

02

Simplification

We will use the following formula :-

The boundaries of the confidence interval

b鈭�t*脳SEbb+t*脳SEb

The slope b1is calculated in the row "Tapping time" and the column "coef" of the following computer output:

b1=鈭�2.6350

In the row "tapping time" and the column "SE Coef" of the given computer output, the computed standard deviation of the slope SEb1is mentioned:

SEb1=0.1769

In the T distribution table, you'll find the crucial.

df鈭�n鈭�2=40鈭�2=38

df=38,as a result, it would use the nearest smaller degrees of freedom, df=30, in the column with c=95%: 鈥�t*=2.042

The confidence interval's bounds

b鈭�t*脳SEb=鈭�2.6350鈭�2.042脳0.1769=鈭�2.9962298b+t*脳SEb=鈭�2.6350+2.042脳0.1769=鈭�2.2737702

There are 95% confident that the slope of the regression line is between -2.9962298 and -2.2737702.

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Most popular questions from this chapter

Tattoos: What per cent of U.S. adults have one or more tattoos? The Harris Poll conducted an online survey of 2302adults and found 29% of respondents had at least 1 tattoo. According to the published report, 鈥淩espondents for this survey were selected from among those who have agreed to participate in Harris Interactive surveys.鈥� Explain why it would not be appropriate to use these data to construct a 95% confidence interval for the proportion of all U.S. adults who have tattoos.

Boyle's law If you have taken a chemistry or physics class, then you are probably familiar with Boyle's law: for gas in a confined space kept at a constant temperature, pressure times volume is a constant (in symbols, PV=kPV=k). Students in a chemistry class collected data on pressure and volume using a syringe and a pressure probe. If the true relationship between the pressure and volume of the gas is PV=k,PV=k, then

P=k1VP=k1V

Here is a graph of pressure versus a volume, 1volume, along with output from a linear regression analysis using these variables:

a. Give the equation of the least-squares regression line. Define any variables you use.

b. Use the model from part (a) to predict the pressure in the syringe when the volume is 17cubic centimeters.

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Exercises T12.4鈥揟12.8 refer to the following setting. An old saying in golf is 鈥淵ou drive for show and you putt for dough.鈥� The point is that good putting is more important than long driving for shooting low scores and hence winning money. To see if this is the case, data from a random sample of 69 of the nearly 1000 players on the PGA Tour鈥檚 world money list are examined. The average number of putts per hole (fewer is better) and the player鈥檚 total winnings for the previous season are recorded and a least-squares regression line was fitted to the data. Assume the conditions for inference about the slope are met. Here is computer output from the regression analysis:

T12.7 Which of the following is the 95% confidence interval for the slope 尾1 of the population regression line?
a. 7,897,179卤3,023,782
b. 7,897,179卤2.000(3,023,782)
c. 鈭�4,139,198卤1,698,371
d. 鈭�4,139,198卤1.960(1,698,371)
e. 鈭�4,139,198卤2.000(1,698,371)

Killing bacteria Expose marine bacteria to X-rays for time periods from 1to 15minutes. Here is a scatterplot showing the number of surviving bacteria (in hundreds) on a culture plate after each exposure time:


a. Below is a scatterplot of the natural logarithm of the number of surviving bacteria versus time. Based on this graph, explain why it would be reasonable to use an exponential model to describe the relationship between the count of bacteria and the time.


b). Here is the output from a linear regression analysis of the transformed data. Give the equation of the least-squares regression line. Be sure to defne any variables you use.

c. Use your model to predict the number of surviving bacteria after 17minutes.
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