Question

the maintenance crew of a hotel must monitor the temperature of the hotel pool and hot tub. to enhance comfort, the management team requests that the mean pool temperature and the mean hot tub temperatures not differ by more than 15 degrees. to estimate the difference in these mean temperatures the maintenance crew selects a random sample of 8 times for checking the hot tub temperature and a random sample of 10 times for checking the pool temperature. although the sample sizes are small, the distribution of temperature for the pool and for the hot tub does not show strong skewness or any outliers. are the conditions for inference met? yes, all three conditions for inference are met. no, the random condition is not met for both samples. no, the 10% condition is not met for both samples. no, the normal/large sample condition is not met for both samples.

Answer 1

Using the Central Limit Theorem, it is found that the correct option is given by:

yes, all three conditions for inference are met.

What are the three conditions for inference?

They are given by:

• Independent samples.

• Random samples.

• Normally distributed samples.

In this problem, the samples are random and independent, but we have to check the normality by the Central Limit Theorem.

What does the Central Limit Theorem state?

It states that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$.

For a skewed variable, the sampling distribution is also approximately normal, as long as n is at least 30.

In this problem, the samples do not have strong skewness, hence they can be described as normally distributed, hence the normality condition is also respected and the correct option is:

yes, all three conditions for inference are met.

More can be learned about the Central Limit Theorem at brainly.com/question/24663213

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