Question

To pass the time on his travels, Ibn Battuta decides to run a test to see if the mean caravan size passing through a certain outpost is greater than 20 camels. He records the sizes of 7 caravans that pass through, assume that this represents a simple random sample of all caravans. After noticing that a smaller number of caravans are significantly larger than the rest of the population, he concludes the population is quite different from normal. He does not know the population's standard deviation. Which of the following describe which kind of test he should run?
a. He should run a Z-test.
b. He should run a T-test, and approximating it with a normal distribution would be appropriate.
c. He should run a T-test, and approximating it with a normal distribution would be inappropriate.
d. None of the above would be appropriate tests.

Answer 1

Answer:

C. He should run a T-test, and approximating it with a normal distribution would be inappropriate.

Step-by-step explanation:

We are told that the standard deviation is unknown.

Now in statistics, when we know the standard deviation, then we use a Z-test but when we don't know the standard deviation, then we will use a t-test.

Now, the t-test assumes a normal distribution for difference in mean of samples but it doesn't assume so for population.

Thus, we will run a t-test and doesn't need to approximate with a normal distribution.