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Chapter 7: Q. 17 (page 456)

Cold cabin? The dotplot shows the results of taking 300SRSs of 10temperature readings from a Normal population with 渭渭=50and 蟽蟽=3and recording the sample standard deviation sxsxeach time. Suppose that the standard deviation from an actual sample is sx=5掳F.sx=5掳F. What would you conclude about the thermostat manufacturer's claim? Explain your reasoning.

Short Answer

Expert verified

It is clear from the convincing evidence that the claim by the manufacturer is false.

Step by step solution

01

Given information

We need to find out whether the manufacturer's claim is true or false.

02

Explanation

A sample standard deviation of temperature for a simple random sample (SRS) with 10temperature readings is represented by each dot in the provided dotplot.

In the above dotplot, there are no dots above 5掳F, nor are there any dots to the right of 5. This means that the sample standard deviation is very unlikely to be s=5 when the population standard deviation is actually 蟽=3, and we'd be shocked if we got a sample with sample standard deviation s=5掳F.

This suggests that there is strong proof that the manufacturer's claim is untrue.

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Most popular questions from this chapter

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 variability of the sampling distribution of the sample mean decreases." Is the student right? Explain your answer.

Tall girls According to the National Center for Health Statistics, the distribution of height for 16-year-old females is modeled well by a Normal density curve with mean 渭=64inches and standard deviation 蟽=2.5inches. Assume this claim is true for the three hundred 16-year-old females at a large high school.

a. Make a graph of the population distribution.

b. Imagine one possible SRS of size 20from this population. Sketch a dotplot of the distribution of sample data.

Suppose we roll a fair die four times. What is the probability that a 6 occurs on exactly one of the rolls?

a.4(16)3(56)14163561b.(16)3(56)1163561c.4(16)1(56)3161563d.(16)1(56)3161563e.6(16)1(56)36161563

A researcher initially plans to take an SRS of size 160 from a certain population and calculate the sample mean x-x炉. Later, the researcher decides to increase the sample size so that the standard deviation of the sampling distribution of x-x炉will be half as big as when using a sample size of 160 . What sample size should the researcher use?

a. 40

b. 80

c. 320

d. 640

e. There is not enough information to determine the sample size.

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 to reveal her attitude toward the product. You think there may be large differences in the responses of women who are employed and those who are not. Because of these differences, you should use

a. a block design, but not a matched pairs design.

b. a completely randomized design.

c. a matched pairs design.

d. a simple random sample.

e. a stratified random sample.
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