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Chapter 7: Q.5 (page 429)

1) State whether it is a parameter or a statistic and (2)use appropriate notation to describe each

number; for example, p = 0.65.

Get your bearings A large container of ball bearings has mean diameter 2.5003 centimeters (cm). This is within the specifications for acceptance of the container by the purchaser. By chance, an inspector chooses 100 bearings from the container that have a mean diameter of 2.5009 cm. Because this is outside the

Short Answer

Expert verified

1)The given statement is a parameter

2)The notation of the population mean is 2.5003 and the notation of sample mean is x炉=2.5009

Step by step solution

01

Part (1) Step 1: Given Information 

Mean diameter of the container centimeters =2.5003

Mean diameter of the 100 bearings =2.5009centimeters

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 mean diameter of the large container serves as an expressive measure for a population in this case. This implies that it is neither a statistic nor a parameter.

Also, the population means is,渭=2.5003渭=2.5003.

03

Part (2) Step 1: Given Information

Mean diameter of the container =2.5003centimeters

Mean diameter of the 100 bearings =2.5009centimeters

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 average diameter of 100 bearings from the large container is used as an expressive metric for a sample in this case.

Also, the sample mean is, x炉=2.5009and the population mean is, 渭=2.5003.

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Most popular questions from this chapter

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.

A study of voting chose 663registered voters at random shortly after an election. Of these, 72%said they had voted in the election. Election records show that only56% of registered voters voted in the election. Which of the following statements is true about the boldface numbers?

(a)72%is a sample; 56%is a population.

(b) 72%and56% are both statistics.

(c)72%is a statistic and 56%is a parameter.

(d) 72%is a parameter and 56%is a statistic.

(e) 72%and56% are both parameters.

A researcher initially plans to take anSRS of size n from a population that has a mean of 80 and a standard deviation of 20. If he were to double his sample size (to 2n), the standard deviation of the sampling distribution of the sample mean would be multiplied by

(a) 2.

(b)12 .

(c) 2.

(d) 12.

(e)12n

According to the U.S. census, the proportion of adults in a certain county who owned their own home was 0.71. An SRS of 100adults in a certain section of the county found that65 owned their home. Which one
of the following represents the approximate probability of obtaining a sample of 100adults in which fewer than 65own their home, assuming that this section of the county has the same overall proportion of adults who own their home as does the entire county?

(a) 10065(0.71)65(0.29)35

(b) 10065(0.29)65(0.71)35
(c) Pz<0.65-0.71(0.71)(0.29)100

(d) Pz<0.65-0.71(0.65)(0.35)100
(e) Pz<0.65-0.71(0.71)(0.29)100

The histogram above left shows the intervals (in minutes) between eruptions of the Old Faithful geyser for all 222recorded eruptions during a particular month. For this population, the median is 75minutes. We used Fathom software to take 500SRSs of size 10from the population. The 500values of the sample median are displayed in the histogram above right. The mean of the 500sample median values is 73.5.

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

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