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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 μμ=50and σσ=3and recording the sample standard deviation sxsxeach time. Suppose that the standard deviation from an actual sample is sx=5°F.sx=5°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°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 σ=3, and we'd be shocked if we got a sample with sample standard deviation s=5°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

Sample proportions List all 6possible SRSS of size n=2, calculate the proportion of red cars in the sample, and display the sampling distribution of the sample proportion on a dotplot. Is the sample proportion an unbiased estimator of the population proportion? Explain your answer.

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