Question

To test the hypothesis that the population standard deviation sigma=4.9, a sample size n=25 yields a sample standard deviation 3.437. Calculate the P-value and choose the correct conclusion.

Your answer:
	The P-value 0.018 is not significant and so does not strongly suggest that sigma<4.9.
	The P-value 0.018 is significant and so strongly suggests that sigma<4.9.
	The P-value 0.028 is not significant and so does not strongly suggest that sigma<4.9.
	The P-value 0.028 is significant and so strongly suggests that sigma<4.9.
	The P-value 0.218 is not significant and so does not strongly suggest that sigma<4.9.
	The P-value 0.218 is significant and so strongly suggests that sigma<4.9.
	The P-value 0.374 is not significant and so does not strongly suggest that sigma<4.9.
	The P-value 0.374 is significant and so strongly suggests that sigma<4.9.
	The P-value 0.025 is not significant and so does not strongly suggest that sigma<4.9.
	The P-value 0.025 is significant and so strongly suggests that sigma<4.9.

Answer 1

The P-value 0.018 is significant and so strongly suggests that sigma<4.9.

Solution:

From given information, we have

The test statistic formula is given as below:

Chi-square = (n – 1)*S^2/ σ2

From given data, we have

n = 25

S = 3.437

σ = 4.9

Chi-square =(25 - 1)*3.437^2 / 4.9^2

Chi-square = 11.8080

We assume

Level of significance = α = 0.05

df = n – 1

df = 25 - 1 = 24

P-value = 0.0180

(by using Chi square table or excel)

P-value < α = 0.05

So, we reject the null hypothesis