A 99% confidence interval for the average time to complete a task among all midd

Question

A 99% confidence interval for the average time to complete a task among all middle school children was (1.4 seconds, 5.6 seconds). The confidence interval was based on data collected from a sample of 50 middle school children from a particular school in a large city. The distribution of sample means must be normal for us to use the t-methods to construct the confidence interval. Is the distribution of sample means normal?

a) As long as the sample data are not heavily skewed, yes since the sample size is more than 30.

b) No because we are not told if the population data follow a normal distribution and the population data must follow a normal distribution for the sample means to be normally distributed regardless of the sample size.

c) No since a random sample wasn’t taken.

d)Yes. Because a sample size of more than 30 guarantees the population data are normally distributed. The only way the sample means will be normally distributed is if the population data are normally distributed.

e) No since the sample size is more than 30.

Explanation / Answer

a) As long as the sample data are not heavily skewed, yes since the sample size is more than 30.

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