Question

You are still upset because your roommate takes pretty long showers, and this reflects negatively on your water bill. you think that their showers last on average 20 minutes. they think you are exaggerating. you record the duration of 36 random showers they take. they have a mean of 19 minutes and a standard deviation of 3.55 minutes.

define the parameter of interest and the appropriate null and alternative hypotheses.

Answer 1

The parameter of interest is the mean duration of showers. Null (\(H_0\)): Mean duration equals 20 mins. Alternative (\(H_1\)): Mean duration differs from 20 mins. Sample data assesses if there's significant evidence for this difference.

In this scenario, the parameter of interest is the average duration of showers taken by your roommate. The null hypothesis
`(\(H_0\))` states that the mean shower duration is equal to 20 minutes, while the alternative hypothesis
`(\(H_1\))` suggests that the mean duration differs from 20 minutes.

By formulating these hypotheses, you aim to investigate whether your roommate's showers indeed differ significantly from your claimed average of 20 minutes. The sample data, with a mean of 19 minutes and a standard deviation of 3.55 minutes from 36 recorded showers.

The hypothesis test aims to determine if the observed difference in the sample mean is statistically significant enough to suggest a true deviation from the claimed average of 20 minutes.