The owner of a smart watch would like to estimate the mean number of steps they take per day. To do so, they select a random sample of 30 days from the previous year’s data and record the number of steps they took on each of those days. Are the conditions for constructing a t confidence interval met?

The days were selected randomly, so the random condition is met. The sample of 30 days is less than 10% of the roughly 365 days in the year, and a sample size of 30 is generally large enough for the t procedure’s Normal/large-sample condition. Therefore, the conditions for constructing a t confidence interval are met.

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