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Chapter 7: Q.6 (page 429)

For each boldface number in Exercises 5 to 8, (1) state whether it is a parameter or a statistic and (2) use appropriate notation to describe each number; for example, p = 0.65

Florida voters Florida has played a key role in recent presidential elections. Voter registration records show that 41% of Florida voters are registered as Democrats. To test a random digit dialing device, you use it to call 250 randomly chosen residential telephones in Florida. Of the registered voters contacted, 33% are registered, Democrats

Short Answer

Expert verified

1) The Given statement is a parameter

2) The notation of the population proportion is p=0.41and the notation of the sample proportion isp^=0.33.p^=0.33

Step by step solution

01

Part (1) Step 1: Given Information 

Voters registered as Democrats=41%

Registered Democrats of the voters contacted=33%

02

Part (1) Step 2: Explanation 

A parameter is an expressive measure for a population, as we all know. A statistic is also a term for an expressive measure for a sample.

The number of Democratic voters is an expressive metric of a population in this case. This implies that it is neither a statistic nor a parameter.

Also, the population proportion is:

p=41%=0.41

Hence, the statement is a parameter.

03

Part (2) Step 1:  Given Information 

Voters registered as Democrats=41%

Registered Democrats of the voters contacted=33%=33%

04

Part (2) Step 2: Explanation 

A parameter is an expressive measure for a population, as we all know. A statistic is also a term for an expressive measure for a sample.

The registered Democrats of the voters were approached for the sample via an expressive measure.

Also, the sample proportion is,

p^=33%=0.33and the population proportion is,p=41%=0.41

Hence, the notation of the population proportion is p=0.41and the notation of the sample proportion is p^=0.33

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Most popular questions from this chapter

Suppose that you are a student aide in the library and agree to be paid according to the 鈥渞andom pay鈥� system. Each week, the librarian flips a coin. If the coin comes up heads, your pay for the week is \(80. If it comes up tails, your pay for the week is \)40. You work for the library for 100 weeks. Suppose we choose an SRS of 2 weeks and calculate your average earnings x. The shape of the sampling distribution of xwill be

(a) Normal.

(b) approximately Normal

(c) right-skewed

(d) left-skewed.

(e) symmetric but not Normal.

IRS audits The Internal Revenue Service plans to examine an SRS of individual federal income tax returns from each state. One variable of interest is the proportion of returns claiming itemized deductions. The total number of tax returns in each state varies from over 15 million in California to about 240,000in Wyoming.

(a) Will the sampling variability of the sample proportion change from state to state if an SRS of 2000tax returns is selected in each state? Explain your answer.

(b) Will the sampling variability of the sample proportion change from state to state if an SRS of 1%of all tax returns is selected in each state? Explain your answer

A sample survey interviews an SRS of 267college women. Suppose (as is roughly true) that 70%of college women have been on a diet within the past12months. What is the probability that 75%or more of the women in the sample have been on a diet? Follow the four-step process.

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Is the sample median an unbiased estimator of the population median? Justify your answer

Increasing the sample size of an opinion poll will

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(e) all of the above.
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