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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

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.

More sample proportions List all 4possible SRSs of size n=3, calculate the proportion of red cars in the sample, and display the sampling distribution of the sample proportion on a dot plot with the same scale as the dot plot in Exercise 19. How does the variability of this sampling distribution compare with the variability of the sampling distribution from Exercise 19? What does this indicate about increasing the sample size?

From exercise19:

Car NumberColorAge
1
Red
1
2
White
5
3
Silver
8
4
Red
20

According to government data, 22% of American children under the age of 6 live in households with incomes less than the official poverty level. A study of learning in early childhood chooses an SRS of 300 children from one state and finds that p鈭�p^=0.29.

a. Find the probability that at least 29% of the sample are from poverty-level households, assuming that 22% of all children under the age of 6 in this state live in poverty-level households.

b. Based on your answer to part (a), is there convincing evidence that the percentage of children under the age of 6 living in households with incomes less than the official poverty level in this state is greater than the national value of 22%? Explain your reasoning.

A researcher initially plans to take an SRS of size 160 from a certain population and calculate the sample mean x-x炉. Later, the researcher decides to increase the sample size so that the standard deviation of the sampling distribution of x-x炉will be half as big as when using a sample size of 160 . What sample size should the researcher use?

a. 40

b. 80

c. 320

d. 640

e. There is not enough information to determine the sample size.

The five-number summary for a data set is given by min = 5, Q1=18, median = 20, Q3=40, max = 75. If you wanted to construct a boxplot for the data set that would show outliers, if any existed, what would be the maximum possible length of the right-side 鈥渨hisker鈥�?

a. 33

b. 35

c. 45

d. 53

e. 55
See all solutions

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