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Cold cabin? The Fathom screenshot below shows the results of taking 500SRSs of 10temperature readings from a population distribution that鈥檚 N(50,3)and recording the sample minimum each time.

(a) Describe the approximate sampling distribution.

(b) Suppose that the minimum of an actual sample is 40F. What would you conclude about the thermostat manufacturer鈥檚 claim? Explain.

Short Answer

Expert verified

a). The sampling distribution is roughly symmetric.

b). The claim appears to be false.

Step by step solution

01

Part (a) Step 1: Given Information

The Fathom screenshot below shows the results of taking 500 SRSs of 10 temperature.

02

Part (a) Step 2: Explanation 

The sample distribution is roughly symmetric. Because the dot plot contains the largest columns of dots roughly in the middle

Because the Centre of a symmetric distribution is roughly at the highest point of the graph, the sampling distribution is centered at around45F,

The range of values is from roughly 39Fto 50F.

03

Part (b) Step 1: Given Information 

The Fathom screenshot below shows the results of taking 500 SRSs of 10 temperature

04

Part (b) Step 2: Explanation 

If the manufacturer's claim is correct, the dot plot will show the approximate sampling distribution.

We can see that there are no dots above 40and only 1 dot to its left, implying that obtaining a sample minimum of 40is extremely unlikely, and hence the manufacturer's claim appears to be untrue.

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