/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q.43 Killing bacteria Expose marine b... [FREE SOLUTION] | 91影视

91影视

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.

Short Answer

Expert verified

a). The scatter plot does not have much curvature.

b). The equation of the least-squaresegression line is lny^=5.97316-0.218425x.

c). The expected number of bacteria after 17 minutes is 9.58247 hundred bacteria or 958.247 bacteria.

Step by step solution

01

Part (a) Step 1: Given Information

Given data:

02

Part (a) Step 2: Explanation

The scatter plot does not have much curvature, a linear model between the two variables of the scatter plot would be appropriate. As a result, using a linear relationship between ln(count)and time is reasonable.

ln(count)=a+b(time)

Taking the exponential

count=eln(count)=ea+b(time)=eaeb(time)
03

Part (b) Step 1: Given Information

Given data:

04

Part (b) Step 2: Explanation

General equation of a least square regression line:

y^=b0+b1x

In the row "constant" and the column "Coef" of the computer's output, the calculated constant b0is given.

b0=5.97316

In the row "Time" and the column "Coef" of the computer output, the slope b1is found.

b1=-0.218425

05

Part (b) Step 3: Explanation

Substituting the value of b0and b1:

y^=b0+b1x

y^=5.97316-0.218425x

Where xrepresents the current time and yis the ln (count)

lny^=5.97316-0.218425x
06

Part (c) Step 1: Given Information

Given data:

07

Part (c) Step 2: Explanation

Substituting the value of x:

lny^=5.97316-0.218425x

lny^=5.97316-0.218425(17)

lny^=2.259935

Taking the exponential

y^=elny^

=e2.259935

=9.58247

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A researcher from the University of California, San Diego, collected data on average per capita wine consumption and heart disease death rate in a random sample of 19 countries for which data were available. The following table displays the data

Is there convincing evidence of a negative linear relationship between wine consumption and heart disease deaths in the population of countries?

Of the 98teachers who responded, 23.5%said that they had one or more tattoos.

a. Construct and interpret a 95%confidence interval for the true proportion of all teachers at the AP institute who would say they have tattoos.

b. Does the interval in part (a) provide convincing evidence that the proportion of all teachers at the institute who would say they have tattoos is different from 0.29. (the value cited in the Harris Poll report)? Justify your answer.

c. Two of the selected teachers refused to respond to the survey. If both of these teachers had responded, could your answer to part (b) have changed? Justify your answer.

T12.9 Which of the following would provide evidence that a power model of the form y=axp, wherep0and p1, describes the relationship between a response variable y and an explanatory variable x?
a. A scatterplot of y versus x looks approximately linear.
b. A scatterplot of Iny versus x looks approximately linear.
c. A scatterplot of y versus lnx looks approximately linear.
d. A scatterplot of Iny versus lnx looks approximately linear.
e. None of these

Click-through rates Companies work hard to have their website listed at the top of an Internet search. Is there a relationship between a website鈥檚 position in the results of an Internet search (1=top position,2=2nd position, etc.) and the percentage of people who click on the link for the website? Here are click-through rates for the top 10 positions in searches on a mobile device:

a. Make an appropriate scatterplot for predicting click-through rate from the position. Describe what you see.

b. Use transformations to linearize the relationship. Does the relationship between click-through rate and position seem to follow an exponential model or a power model? Justify your answer.

c. Perform least-squares regression on the transformed data. Give the equation of your regression line. Define any variables you use.

d. Use your model from part (c) to predict the click-through rate for a website in the 11th position.

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:

T12.8 Which of the following would make the calculation in Exercise T12.7 invalid?

a. If the scatterplot of the sample data wasn鈥檛 perfectly linear.

b. If the distribution of earnings has an outlier.

c. If the distribution of earnings wasn鈥檛 approximately Normal.

d. If the earnings for golfers with small putting averages was much more variable than the earnings for golfers with large putting averages.

e. If the standard deviation of earnings is much larger than the standard deviation of putting average.

See all solutions

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.