Question

A proup of atudents estimated the iength of one finute whthoue reforerse ss a watch or cisck, and the timas (secondi) are fisted below. Use a 0.10 significance levei to test the claim that these times are from a population with a mean equal to eo seconct. Does z appear that stodens are reasonstiy paod as estinating one minute? Attaming bi condionons for conducting a typothesis test are met, what are the null and ahemative hypotheses?

Answer 1

To determine if students' estimates of one minute are accurate, we set up a hypothesis test with the null hypothesis stating the mean is 60 seconds, and the alternative stating otherwise. We use a 0.10 significance level and assume normal distribution for the test.

Step-by-step explanation:

To conduct a hypothesis test to determine if the times estimated by students for the length of one minute are from a population with a mean equal to 60 seconds, we set up our null and alternative hypotheses. Using a significance level of 0.10, the null hypothesis (H0) claims that the mean time (μ) is equal to 60 seconds, while the alternative hypothesis (Ha) claims that the mean time is not equal to 60 seconds. The hypotheses would be H0: μ = 60 and Ha: μ ≠ 60.

As this scenario fits the case of testing a single population mean, we assume normality and known population standard deviation in conducting the hypothesis test. If we find our test statistic falls into the rejection region defined by our alpha level of 0.10, we would reject H0. If the test statistic does not fall in the rejection region, we would not reject the null hypothesis, implying that there isn't strong enough evidence to claim that the students' time estimates are different from the standard 60 seconds often associated with estimating one minute.