Question

Strength
279.3	280.7	245.9	269.8	256.9	252.6	257
263.8	265.9	272.5	250.6	255.6	242.5	268.1
274.2	248.2	249.8	265.3	256.1	274	250.3
259.5	283.8	242.2	270.9	265.1	264.7	275.1
257.1	267.4	279.3	243.9	243.3	271.4	261.5
253.4	259.6	259.2	265.4	267.5	267.5	255.5
259.6	252	286.7	256.1	261.9	252.7	267.1

data set 9-3

Comparing the standard deviation of data set 9-3; can you detect a significant difference to a a standard deviation of 15. Provide the P-value (2-sided).

find the p value within excel

Answer 1

Sample Standard deviation calculated using STDEV.S(), s = 11.1458

Sample, size, n = 49

Null and alternative hypothesis:

Hₒ : σ = 15

H₁ : σ ≠ 15

Test statistic:

χ² = (n-1)s² / σ² = (49 - 1)11.1458² /15² = 26.5023

Degree of freedom:

Df = n -1 = 49 - 1 = 48

p-value = 1-CHISQ.DIST.RT(26.5023, 48) = 0.0050

Decision:

p-value < α, Reject the null hypothesis.