Applications for the Chi-Square Test for a Variance or Standard Deviation

1.  Calories in Pancake Syrup A nutritionist claims that the standard deviation of the number of calories in 1 tablespoon of the major brands of pancake syrup is 60.  A sample of major brands of syrup is selected, and the number of calories is shown.  At α = 0.10, can the claim be rejected?

53	210	100	200	100	220
210	100	240	200	100	210
100	210	100	210	100	60

Answer:

H₀: σ = 60 (claim) and H₁: σ ≠ 60; C.V. = 8.672; 27.587; d.f. 17; X² = 19.707; do not reject the null hypothesis.  There is not enough evidence to reject the claim that the standard deviation is 60.

2.    Transferring Phone Calls The manager of a large company claims that the standard deviation of the time (in minutes) that it takes a telephone call to be transferred to the correct office in her company is 1.2 minutes or less.  A sample of 15 calls is selected, and the calls are timed.  The standard deviation of the sample is 1.8 minutes.  At α = 0.01, test the claim that the standard deviation is less than or equal to 1.2 minutes.  Use the P-value method.

Answer:

H₀: σ ≤ 1.2 (claim) and H₁: σ > 1.2; α = 0.01; d.f.= 11; X² = 9.0425; do not reject the null hypothesis.  There is enough evidence to support the claim that the standard deviation is less than or equal to 1.2 minutes.

3.      Calories in Doughnuts A random sample of 20 different kinds of doughnuts had the following calorie counts.  At α = 0.01, is there sufficient evidence to conclude that the standard deviation is greater than 20 calories?

290	320	260	220	300	310	310	270	250	230
270	260	310	200	250	250	270	210	260	300

Answer:

H₀: σ ≤ 20 and H₁: σ > 20 (claim); C.V. = 36.191; d.f. = 19; X² = 58.5502; reject the null hypothesis.  There is enough evidence to support the claim that the standard deviation is greater than 20.

by: Marie Louissie Ynez U. Lavega