Question

Assume that the average volume of raindrops globally is normally
distributed with mean 0.45 ml and variance 0.01 ml^{2}.
Michael measures the volume of two raindrop at Rainyville as 0.65
ml and 0.75 ml; and comes to believe that the raindrops at
Rainyville are significantly larger than the global average at the
5% level.

Which statistical test should Michael use and why?

A. The Z-test because population standard deviation is known.

B. The T-test because the population standard deviation is unknown.

C. The Z-test because population standard deviation is unknown.

D. The T-test because population standard deviation is known.

Answer #1

Solution

Given,

= 0.45 (population mean)

= 0.01 (population SD)

Claim by Michel is is significantly greater than 0.45

Hypothesis are

H0: = 0.45 vs H1: > 0.45

Since the population SD is known , we use z test

So answer is

A. The Z test, because the population standard deviations is known.

(If unknown, then use t test)

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