Choosing and calculating test statistics for hypothesis tests on the...
We want to conduct a hypothesis test of the claim that the population mean germination time of strawberry seeds is different from 18.8 days. So, we choose a random sample of strawberries. The sample has a mean of 19 days and a standard deviation of 1.1 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 90 , and it is from a non-normally distributed population with a known standard deviation of 0.9 .
$z=\square$
$t=\square$
It is unclear which test statistic to use.
(b) The sample has size 20 , and it is from a population with a distribution about which we know very little.
$z=\square$
$t=\square$
It is unclear which test statistic to use.

Step 1 ：We are given two scenarios for which we need to calculate the test statistics. The test statistic is a measure that helps us decide whether to reject or not reject the null hypothesis in a hypothesis test.

Step 2 ：In the first scenario, we have a sample size of 90 from a non-normally distributed population with a known standard deviation. In this case, we can use the z-test statistic because the sample size is large (greater than 30) and the population standard deviation is known. The formula for the z-test statistic is \((\text{sample mean} - \text{population mean}) / (\text{population standard deviation} / \sqrt{\text{sample size}})\).

Step 3 ：Substituting the given values into the formula, we get \(z = (19 - 18.8) / (0.9 / \sqrt{90})\). Calculating this gives us a z-test statistic of approximately 2.11.

Step 4 ：In the second scenario, we have a sample size of 20 from a population about which we know very little. In this case, we can use the t-test statistic because the sample size is small (less than 30) and we don't know the population standard deviation. The formula for the t-test statistic is \((\text{sample mean} - \text{population mean}) / (\text{sample standard deviation} / \sqrt{\text{sample size}})\).

Step 5 ：Substituting the given values into the formula, we get \(t = (19 - 18.8) / (1.1 / \sqrt{20})\). Calculating this gives us a t-test statistic of approximately 0.81.

Step 6 ：Final Answer: For scenario (a), the z-test statistic is \(\boxed{2.11}\). For scenario (b), the t-test statistic is \(\boxed{0.81}\).