Question

Q2) On average, hot-tubs typically take 15 minutes to “heat-up.” A certain hot-tub manufacturer advertises that its heating equipment can heat a tub in less than 15 minutes. A random sample of 40 tubs of this brand is selected, and the heat-up time was determined for each tub. From the sample, the average heat-up time was ?̅ = 13.9 minutes and the sample standard deviation was ? = 3.2 minutes. Does the data support the company’s claim that its equipment can, on average, heat a tub in less than 15 minutes?

a) Test the claim above using a hypothesis test and an alpha-level of 0.05.

b) Repeat the test using an alpha-level of 0.01.

Answer 1

a) Test the claim above using a hypothesis test and an alpha-level of 0.05.

The hypothesis being tested is:

H0: µ = 15

Ha: µ < 15

15.000	hypothesized value
13.900	mean 1
3.200	std. dev.
0.506	std. error
40	n
39	df
-2.174	t
.0179	p-value (one-tailed, lower)

The p-value is 0.0179.

Since the p-value (0.0179) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that heating equipment can heat a tub in less than 15 minutes.

b) Repeat the test using an alpha-level of 0.01.

The p-value is 0.0179.

Since the p-value (0.0179) is greater than the significance level (0.01), we fail to reject the null hypothesis.

Therefore, we cannot conclude that heating equipment can heat a tub in less than 15 minutes.

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