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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

The amount that households pay service providers for access to the Internet varies quite a bit, but the mean monthly fee is 50\( and the standard deviation is 20\). The distribution is not Normal: many households pay a low rate as part of a bundle with phone or television service, but some pay much more for Internet only or for faster connections. 11 A sample survey asks an SRS of 50 households with Internet access how much they pay. Let x-x炉be the mean amount paid.

a. Explain why you can't determine the probability that the amount a randomly selected household pays for access to the Internet exceeds 55 .\(

b. What are the mean and standard deviation of the sampling distribution of x-x炉?

c. What is the shape of the sampling distribution of x-x炉? Justify your answer.

d. Find the probability that the average fee paid by the sample of households exceeds 55 .\)

The central limit theorem is important in statistics because it allows us to use a Normal distribution to find probabilities involving the sample mean if the

a. sample size is reasonably large (for any population).

b. population is Normally distributed (for any sample size).

c. population is Normally distributed and the sample size is reasonably large.

d. population is Normally distributed and the population standard deviation is known (for any sample size).

e. population size is reasonably large (whether the population distribution is known or not).

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.

At a particular college, 78%of all students are receiving some kind of financial aid. The school newspaper selects a random sample of 100students and 72%of the respondents say they are receiving some sort of financial aid. Which of the following is true?

  1. 78%is a population and 72%is a sample.
  2. 72%is a population and 78%is a sample.
  3. 78%is a parameter and 72%is a statistic.
  4. 72%is a parameter and 78%is a statistic.
  5. 72%is a parameter and 100is a statistic.

The distribution of grade point average for students at a large high school is skewed to the left with a mean of 3.53 and a standard deviation of 1.02.

a. Describe the shape of the sampling distribution of x炉 for SRSs of size n = 4 from the population of students at this high school. Justify your answer.

b. Describe the shape of the sampling distribution of x炉 for SRSs of size n = 50 from the Page Number: 480 population of students at this high school. Justify your answer.
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