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?

He should run a Z-test.

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

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

None of the above would be appropriate tests.

Answer 1

If population standard deviation is unknown we can't use z test.

For approximation to normality by using central limit theorm minimum sample size required is 30 which is a thumb rule.

Therefore, with sample size of 7 we can't assume normality.

Without normality assumptions we can't run a t test. Because they test is the basic assumption of normality.

Therefore, correct option is None of the above would be appropriate test.

Tha above problem can be solved using non parameteric tests.

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