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Chapter 7: Q. 11 (page 455)

Doing homework A school newspaper article claims that 60%of the students at a large high school completed their assigned homework last week. Assume that this claim is true for the 2000students at the school.

a. Make a bar graph of the population distribution.

b. Imagine one possible SRS of size 100from this population. Sketch a bar graph of the distribution of sample data.

Short Answer

Expert verified

a. The bar graph :

b. The bar graph is

Step by step solution

01

Part(a) Step 1 : Given information

We need to make bar graph for the students doing homework or not.

02

Part(a) Step 2 : Simplify

As we know, 60%student completed homework. Therefore,

100%-60%=40%students did not complete their work.

So, in bar graph the width of bars will be equal and height of bars should be equal to their percentage.

The bar graph is

03

Part(b) Step 1 : Given information

We need to draw bar graph for one possible SRS of 100 from total population.

04

Part(b) Step 2 : Simplify

As we know, 60% students completed their work. Now,

We have 100students in a random sample, so it means nearly 60%students did their work but not exact 60.

Lets take an example , it is possible that 57students did their work.

Now, the width of bar graphs would be same and height will be equal to their respective frequencies.

The frequency bar graph is :

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Most popular questions from this chapter

Social scientists are interested in the association between high school graduation rate (HSGR, measured as a percent) and the percent of U.S. families living in poverty (POV). Data were collected from all 50 states and the District of Columbia, and a regression analysis was conducted.

The resulting least-squares regression line is given by POV∧=59.2-0.620(HSGR) POV^=59.2-0.620(HSGR) with r2=0.802r2=0.802. Based on the information, which of the following is the best interpretation for the slope of the least-squares regression line?

a. For each 1% increase in the graduation rate, the percent of families living in poverty is predicted to decrease by approximately 0.896 .

b. For each 1 % increase in the graduation rate, the percent of families living in poverty is predicted to decrease by approximately 0.802.

c. For each 1 % increase in the graduation rate, the percent of families living in poverty is predicted to decrease by approximately 0.620.

d. For each 1 % increase in the percent of families living in poverty, the graduation rate is predicted to decrease by approximately 0.802.

e. For each 1 % increase in the percent of families living in poverty, the graduation rate is predicted to decrease by approximately 0.620.

Finch beaks One dimension of bird beaks is "depth"-the height of the beak where it arises from the bird's head. During a research study on one island in the Galapagos archipelago, the beak depth of all Medium Ground Finches on the island was found to be Normally distributed with mean μ=9.5 millimeters(mm)and standard deviation σ=1.0mm.

a. Choose an SRS of 5 Medium Ground Finches from this population. Describe the sampling distribution of x¯.

b. Find the probability that x¯estimates μwithin ±0.5mm. (This is the probability that x¯takes a value between 9 and 10 mm.

c. Choose an SRS of 50 Medium Ground Finches from this population. Now what is the probability that x¯falls within ±0.05mmof μ? In what sense is the larger sample "better"?

Bad eggs Selling eggs that are contaminated with salmonella can cause food poisoning in consumers. A large egg producer randomly selects 200 eggs from all the eggs shipped in one day. The laboratory reports that 9 of these eggs had salmonella contamination. Identify the population, the parameter, the sample, and the statistic.

The Gallup Poll has decided to increase the size of its random sample of voters from about 1500 people to about 4000 people right before an election. The poll is designed to estimate the proportion of voters who favor a new law banning smoking in public buildings. The effect of this increase is to

a. reduce the bias of the estimate.

b. increase the bias of the estimate.

c. reduce the variability of the estimate.

d. increase the variability of the estimate.

e. reduce the bias and variability of the estimate.

Sample proportions List all 10possible SRSs of size n=2, calculate the proportion of females for each sample, and display the sampling distribution of the sample proportion on a dotplot.
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