Question

Cold cabin? The dotplot shows the results of taking $300$SRSs of $10$temperature readings from a Normal population with ${\mu }^{\mu }=50$and ${\sigma }^{\sigma }=3$and recording the sample standard deviation $s{x}^{s_x}$each 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

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

Step-by-step solution

Given information

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

Explanation

A sample standard deviation of temperature for a simple random sample (SRS) with $10$temperature 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 $\sigma =3$, 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.