We want to conduct a hypothesis test of the claim that the population mean germination time of strawberry seeds is different from \( 18.9 \) days. So, we choose a random sample of strawberries. The sample has a mean of 19 days and a standard deviation of \( 1.2 \) 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 16 , and it is from a population with a distribution about which we know very little. \( z= \) \( t= \) It is unclear which test statistic to use. (b) The sample has size 85 , and it is from a non-normally distributed population with a known standard deviation of \( 1.4 \). \( z= \) \( \mathrm{t}= \) It is unclear which test statistic to use.

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Our questions is that we want to conduct a hypothesis test of the claim that the population mean germination time for strawberry seats is different from 18 points nine days. So we choose a random sample of strawberries, the sample had, the sample has a meal of 19 days and a standard division of 1.2 days. So for each of the following sample sampling scenarios choose an appropriate test statistics for our hypothesis tests and the population maintained calculates the test statistics, you're supposed to round your answers to the small place. So the first question says that the sample size Uh the sample has a size of 16 and it is certain population with a distribution which about which we know very later on. So the value of the the type of test statistics we use is dependent on the type of distribution that we have at end. If we have a normal distribution, we use a uh z distribution. But it was stated in our question that we don't know Uh the kind of distribution that defines the population of our dataset. So that simply implies that it is unclear of the test statistics for us to use. So the answer to our question is clear is that it is unclear which states statistics to use. So for question one it is unclear which test statistics to use. So that's the answer to the first question. So the second question is that the sample size, uh the sample has a size of 85 it is from a non normally distributed population with a non standard division of 1.4 so far, question to our end is of course to 85. The population standard deviation is equal to 1.4. We also have that the population mean Is of course to 18.9 Meal is of course to 18.9 and the sample mean expert, We have that to be equals two 19 actually okay, so this is 19. So according to the central limit stadium, when the sample size of the sampling distribution is greater than or equals to 30, that his end is greater than or equals to 30. We can definitely say that the dataset is approximately normally distributed. Hence that the test statistics are going to use for such data set is going to be a normal, a normal distribution or a Z. Test. Also we have the value of the population Standard division since we know the value of the population Standard star division to be caused 1.4, it simply implies that we can also assume that our datasets excuse me, is normally distributed. Hence our test started this in this case of us is going to be a sitter. So we have that Z is a close to X bar minus mu divided by sigma divided by the scrolls of end. The expert is going to be 19 minus, our army is going to be 18 points nine divided by sigma is 1.4 Divided by sprouts of 85. So 19 -18.9 I want to do the mask. We have a 0.1 divided by 14. Excuse Me? Fight it by the scrolls of 85 and that is 0.1519. And when we do the math, 0.1 divided by 0.1519 and that's going to be 0.65 85. So for a second question, our test statistic is going is going to be 0.6585 at the question. So if you keep the one sign to decimal place, so that's approximately 0.66.

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