Question

3). You are given the claim that the mean of a population is not equal to 24 cm. You
don’t believe in this claim and so you want to test it. Suppose that you know the
population standard deviation is 4 cm, and the population distribution is approximately
normal. To test this claim, you take a random sample as follows
X = (20, 23, 22, 24, 24, 24, 25, 26, 24, 23, 27, 24, 29, 20, 25, 26, 28).
Is there enough evidence to support the claim? Justify your answer completely.

Answer 1

Here, we have to use one sample z test for the population mean.

The null and alternative hypotheses are given as below:

H0: µ = 24 versus Ha: µ ≠ 24

This is a two tailed test.

The test statistic formula is given as below:

Z = (Xbar - µ)/[σ/sqrt(n)]

From given data, we have

µ = 24

Xbar = 24.35294118

σ = 4

n = 17

α = 0.05

Critical value = -1.96 and 1.96

(by using z-table or excel)

Z = (24.35294118 - 24)/[4/sqrt(17)]

Z = 0.3638

P-value = 0.7160

(by using Z-table)

P-value > α = 0.05

So, we do not reject the null hypothesis

There is sufficient evidence to conclude that the mean of a population is not equal to 24 cm.