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Cold cabin? The Fathom screen shot below shows the results of taking 500SRSs of 10temperature readings from a population distribution that鈥檚 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鈥檚 claim? Explain

Short Answer

Expert verified

a). The sampling distribution is right-skewed.

b). The claim appears to be false.

Step by step solution

01

Part (a) Step 1: Given Information 

The results of taking 500SRS's of10 temperature.

02

Part (a) Step 2: Explanation

The sampling distribution is right-skewed because the dot plot has the highest columns of dots to the left and a tail to the right.

The sampling distribution is centered at about 9F2, because the center of a right-skewed distribution is slightly to the right of the highest points of the graph.

The range of values is from roughly 2F2 to 27F2.

03

Part (b) Step 1:  Given Information 

The results of taking 500SRS's of 10 temperature.

04

Part (b) Step 2: Explanation 

If the manufacturer's claim is true, then the approximate sampling distribution is given by the dot plot.

We note that no dots are above 25 and only 1 dot is to its right, this means that it is very unlikely to obtain a sample variance of 25 and thus it appears that the manufacturer's claim is false.

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