Final answer:
To determine if the sample estimates the length of a minute well, a hypothesis test using the t-distribution is performed with the null hypothesis being that the population mean is 60 seconds. The test involves calculating the t-statistic and comparing it to critical values at a 0.05 significance level.
Step-by-step explanation:
To test the claim whether the sample of people are reasonably good at estimating a minute (where the population mean is 60 seconds), we perform a hypothesis test.
Step-by-step process:
- State the null hypothesis (H0): The population mean is 60 seconds. (μ = 60).
- State the alternative hypothesis (Ha): The population mean is not 60 seconds. (μ ≠ 60).
- Calculate the sample mean (μ-bar) and the sample standard deviation (s).
- Determine the level of significance, which is given as 0.05.
- Since the sample size is less than 30, and we do not know the population standard deviation, we use the t-distribution.
- Calculate the t-statistic using the formula: t = (μ-bar - μ) / (s / √n), where n is the sample size.
- Find the critical t-value(s) for a two-tailed test with n - 1 degrees of freedom at the 0.05 significance level.
- Compare the calculated t-statistic to the critical t-value(s) to determine if we reject or fail to reject the null hypothesis.
If the t-statistic is within the range of the critical t-values, we fail to reject the null hypothesis, suggesting that the sample mean is not significantly different from 60 seconds. If the t-statistic falls outside this range, we reject the null hypothesis, indicating a significant difference.
By performing these steps, we can assess whether these people are reasonably good at estimating a minute.