getting confused

Question

We want to conduct a hypothesis test of the claim that the population mean germination time of strawberry seeds is different from 18.1 days. So, we choose a random sample of strawberries. The sample has a mean of 18 days and a standard deviation of 1.4 days.

For each of the following sampling scenarios, choose an appropriate test statistic for our hypothesis test on the population mean. Then calculate that statistic. Round your answers to two decimal places.

a-     The sample has size 10, and it is from a normally distributed population with an unknown standard deviation. z: or t:

b-   The sample has size 75, and it is from a non-normally distributed population with a known standard deviation of 1.1. z: or t:

Answer 1

Use a t distribution when you do not know the standard deviation of the population and z when you do. Neither z nor t is appropriate for a non-normal distribution unless n is large (> 30 is often considered a cut-off point) from the Central Limit Theorem. So I would say t (df = 9) and z for a and b.

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