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Chapter 7: Q. 50 (page 454)

A grinding machine in an auto parts plant prepares axles with a target diameter μ=40.125millimeters (mm). The machine has some variability, so the standard deviation of the diameters is σ=0.002mm. The machine operator inspects a random sample of 4axles each hour for quality control purposes and records the sample mean diameter x. Assuming that the process is working properly, what are the mean and standard deviation of the sampling distribution of x? Explain

Short Answer

Expert verified

The mean of the sampling distribution is μx=40.125mm

The standard deviation of the sampling distribution isσx=0.001mm

Step by step solution

01

Given information

σ=0.002mm

μ=40.125mm

Samples taken =4

Find the mean and standard deviation of the sample.

02

Explanation

The given data is

μ=40.125mm

σ=0.002mm

n=4

The population mean is equal to the mean of the sampling distribution of the sample mean x

localid="1650109916424" μx=μ=40.125mm

The standard deviation of the sampling distribution of the sample meanxis calculated by dividing the population standard deviation by the square root of the sample size.

localid="1650109931135" σx=σn=0.0024=0.001mm.

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Most popular questions from this chapter

The Gallup Poll has decided to increase the size of its random sample of voters from about 1500people to about 4000people right before an election. The poll is designed to estimate the proportion of voters who favor a new law banning smoking in public buildings. The effect of this increase is to

(a) reduce the bias of the estimate.

(b) increase the bias of the estimate.

(c) reduce the variability of the estimate.

(d) increase the variability of the estimate.

(e) have no effect since the population size is the same

Cold cabin? The Fathom screen shot below shows the results of taking 500SRSs of 10temperature readings from a population distribution that’s N(50,3)and recording the sample variance 2xeach time.

(a) Describe the approximate sampling distribution.

(b) Suppose that the variance from an actual sample is s2x=25. What would you conclude about the thermostat manufacturer’s claim? Explain

You want to take an SRS 50of the 816students who live in a dormitory on a college campus. You label the students 001to 816in alphabetical order. In the table of random digits, you read the entries

95592 94007 69769 33547 72450 16632 81194 14873

The first three students in your sample have labels

(a) 955,929,400

(b) 400,769,769

(c) 559,294,007

(d) 929,400,769

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3. Describe the shape of the

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 take500SRSs 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.

Sampling distribution. Explain what this means in terms of overestimating or underestimating the population median

You work for an advertising agency that is preparing a new television commercial to appeal to women. You have been asked to design an experiment to compare the effectiveness of three versions of the commercial. Each subject will be shown one of the three versions and then asked about her attitude toward the product. You think there may be large differences between women who are employed and those who are not. Because of these differences, you should use

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