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Chapter 10: Q 1. (page 639)

I want red!A candy maker offers Child and Adult bags of jelly beans with

different color mixes. The company claims that the Child mix has 30%red jelly beans, while the Adult mix contains 15%red jelly beans. Assume that the candy maker鈥檚 claim is true. Suppose we take a random sample of 50jelly beans from the Child mix and a separate random sample of 100jelly beans from the Adult mix. Let p^Cand p^Abe the sample proportions of red jelly beans from the Child and

Adult mixes, respectively.

a. What is the shape of the sampling distribution of p^C-p^A? Why?

b. Find the mean of the sampling distribution.

c. Calculate and interpret the standard deviation of the sampling distribution.

Short Answer

Expert verified

a. The shape in normal.

b. 渭p^C-p^A=0.15

c.蟽p^C-p^A=0.07399

Step by step solution

01

Given Information

It is given that nC=50

nA=100

pC=0.30

pA=0.15

02

Shape of p^C-p^A

Assuming p^C-p^Ais normal.

Condition is:

nCpC鈮�10

nC1-pC鈮�10

nApA鈮�10

nCpC=(50)(0.30)=15

nApA=(100)(0.15)=15

nA1-pA=(100)(1-0.15)=(100)(0.85)=85

The shape is approximately normal as it satisfies all the four conditions.

03

Mean of Sampling Distribution

Using 渭p^C-p^A=pC-pA

=0.30-0.15=0.15

Mean is0.17

04

Standard Deviation

Child jelly(50)<10%of all child jelly beansand

Adult jelly(100)<10%of all adult jelly beans

Standard deviation is 蟽p^C-p^A=pC1-pCnC+pA1-pAnA

=0.30(1-0.30)50+0.15(1-0.15)100

=0.30(0.70)50+0.15(0.85)100鈮�0.07399

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Most popular questions from this chapter

A certain candy has different wrappers for various holidays. During Holiday 1, the candy wrappers are 30%silver, 30%red, and 40%pink. During Holiday 2, the wrappers are 50%silver and 50%blue. In separate random samples of 40candies on Holiday 1and 40candies on Holiday 2, what are the mean and standard deviation of the total number of silver wrappers?

a. 32,18.4

b.32,6.06

c.32,4.29

d.80,18.4

e.80,4.29

Which of the following statements is false?

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d. In a quantitative data set, adding a new data value equal to the mean will decrease the standard deviation.

e. If a distribution of quantitative data is strongly skewed, the median and interquartile range should be reported rather than the mean and standard deviation.

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I. Confirm graphically that the scores of the caffeine drinkers could have come from a Normal distribution.

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The distribution of grade point averages (GPAs) for a certain college is approximately Normal with a mean of 2.5 and a standard deviation of 0.6. The minimum possible GPA is 0.0 and the maximum possible GPA is 4.33. Any student with a GPA less than 1.0 is put on probation, while any student with a GPA of 3.5 or higher is on the dean鈥檚 list. About what percent of students at the college are on probation or on the dean鈥檚 list?

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