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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

Lightning strikes The number of lightning strikes on a square kilometer of open ground in a year has mean 6and standard deviation 2.4. (These values are typical of much of the (United States.) The National lighting Detection Network (NLDN) uses automatic sensors to watch for lightning in a random sample of 10 one-square-kilometer plots of land.

(a) What are the mean and standard deviation of xthe sample mean number of strikes per square kilometers?

(b) Explain why you can't safely calculate the probability that x<5based on a sample of size 10.

(c) Suppose the NLDN takes a random sample of n=50square kilometers instead. Explain how the central limit theorem allows us to find the probability that the mean number of lightning strikes per square kilometer is less than 5. Then calculate this probability. Show your work.

What does the CLT say? Asked what the central limit theorem says, a student replies, "As you take larger and larger samples from a population, the histogram of the sample values looks mote and more Normal." ls the student right? Explain your answer.

Doing homework Refer to Exercise 9.

(a) Make a graph of the population distribution given that there are 3000 students in the school. (Hint: What type of variable is being measured?)

(b) Sketch a possible graph of the distribution of sample data for the SRS of size 100 taken by the AP Statistics students.

The student newspaper at a large university asks an SRS of 250undergraduates, 鈥淒o you favor eliminating the carnival from the term-end celebration?鈥� All in all, 150of the 250are in favor. Suppose that (unknown to you) 55%of all undergraduates favor eliminating the carnival. If you took a very large number of SRSs of size n=250from this population, the sampling distribution of the sample proportion P鈭�would be

(a) exactly Normal with mean 0.55and standard deviation of 0.03

(b) approximately Normal with mean 0.55and standard deviation 0.03.

(c) exactly Normal with mean 0.60and standard deviation 0.03.

(d) approximately Normal with mean 0.60and standard deviation 0.03.

(e) heavily skewed with mean 0.55and standard deviation 0.03.

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

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

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

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

(d) approximately Normal with mean122and standard deviation 5.

(e) approximately Normal with a mean122and standard deviation0.35.
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