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Estimating Mean Germination Time of Strawberry Seeds

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Suppose that we want to estimate the mean germination time of strawberry seeds. The germination times for the sample of strawberries we choose has a mean of days and a standard deviation of days. For each of the following sampling scenarios, determine which test statistic is appropriate to use when making inference statements about the population mean.

(In the table, refers to a variable having a standard normal distribution, and refers to a variable having a t distribution.)
sampling scenario

1. The same has size 85, and it is from a non-normally distributed population.
a. Z
b. T
c. Could use either Z or T
d. Unclear

2. The sample has size 75, and it is from a non-normally distributed population with a known standard deviation of 1.4.
a. Z
b. T
c. Could use either Z or T
d. Unclear

3. The sample has size 20, and it is from a normally distributed population with a known standard deviation of 1.4.
a. Z
b. T
c. Could use either Z or T
d. Unclear

4. The sample has size 14, and it is from a population with a distribution about which we know very little.
a. Z
b. T
c. Could use either Z or T
d. Unclear

5. The sample has size 13, and it is from a normally distributed population with unknown standard deviation.
a. Z
b. T
c. Could use either Z or T
d. Unclear

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This solution briefly discusses the answers for each multiple choice question.

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1. The same has size 85, and it is from a non-normally distributed population.
a. Z
b. T
c. Could use either Z or T
d. Unclear

*sample size is large enough for us to assume the sample mean is distributed normally, So we can use T if the standard deviation is unknown, or Z if the standard deviation is known. (however, the difference is very small)

2. The ...

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