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Chapter 7: Q. 73 (page 481)

The distribution of scores on the mathematics part of the SAT exam in a recent year was approximately Normal with mean 515 and standard deviation 114 . Imagine choosing many SRSs of 100 students who took the exam and averaging their SAT Math scores. Which of the following are the mean and standard deviation of the sampling distribution of x-?x炉?

a. Mean =515,SD=114

b. Mean =515,SD=114/100SD=114/100

c. Mean role="math" localid="1654342976765" =515/100,SD=114/100

d. Mean role="math" localid="1654343050312" =515/100,SD=114/100SD=114/10

e. Cannot be determined without knowing the 100 scores.

Short Answer

Expert verified

The value of Mean =515and SD=114100

The correct option is (b)

Step by step solution

01

Given information 

Given,

渭=515蟽=114n=100
02

Explanation for correct option

Calculation:

渭x炉=渭=515蟽x炉=蟽n=114100

Hence, the correct option is (b)

03

Explanation for incorrect option

(a). mean=515,SD=114are not the mean and standard deviation of the sampling distribution of role="math" localid="1654343011275" x-and role="math" localid="1654343023938" x炉

(c). Mean=515/100,SD=114/100are not the mean and standard deviation of the sampling distribution of role="math" localid="1654343077524" x-and role="math" localid="1654343088243" x炉

(d). Mean=515/100,SD=114/100SD=114/10are not the mean and standard deviation of the sampling distribution of x-and x炉

(e). Cannot be determined without knowing the 100 scores is incorrect statement

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Most popular questions from this chapter

Squirrels and their food supply (3.2) Animal species produce more offspring when their supply of food goes up. Some animals appear able to anticipate unusual food abundance. Red squirrels eat seeds from pinecones, a food source that sometimes has very large crops. Researchers collected data on an index of the abundance of pinecones and the average number of offspring per female over 16years.4Computer output from a least-squares 4regression on these data and a residual plot are shown here

a. Is a linear model appropriate for these data? Explain.

b. Give the equation for the least-squares regression line. Define any variables you use.

c. Interpret the values of r2and sin context.

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.

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 .\)

A statistic is an unbiased estimator of a parameter when

a. the statistic is calculated from a random sample.

b. in a single sample, the value of the statistic is equal to the value of the parameter.

c. in many samples, the values of the statistic are very close to the value of the

parameter.

d. in many samples, the values of the statistic are centered at the value of the parameter.

e. in many samples, the distribution of the statistic has a shape that is approximately

Normal.

In a certain large population of adults, the distribution of IQ scores is strongly left skewed with a mean of 122 and a standard deviation of 5. Suppose 200 adults are randomly selected from this population for a market research study. For SRSs of size 200, the distribution of sample mean IQ score is

a. left-skewed with mean 122 and standard deviation 0.35.

b. exactly Normal with mean 122 and standard deviation 5.

c. exactly Normal with mean 122 and standard deviation 0.35.

d. approximately Normal with mean 122 and standard deviation 5.

e. approximately Normal with mean 122 and standard deviation 0.35.
See all solutions

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