Question

It is often thought that there is indeed a “cold season”. To test this theory, we sampled 200 people in April when cold season is thought to be over and again in September at the peak of cold season. We measured if they were sick with a cold (one or more times) during the month of April and again during the month of September. Below is the respective data collected. Use this data and conduct a hypothesis test to assess if there is difference in cold prevalence during (in September) and outside of cold season (April).

	Cold during September
Cold during April	Yes	No
Yes	15	30
No	29	127

Answer 1

Solve using Excel by conduting a chi-square test:

	ACTUAL
	Cold During September Yes	Cold During September No	Total
Cold During April Yes	15	30	45
Cold During April No	29	127	156
Total	44	157	201
	EXPECTED
	Cold During September Yes	Cold During September No		FORMULA FOR EXPECTED VALUE
Cold During April Yes	9.85	35.15		=(B$5*$D3)/$D$5	=(C$5*$D3)/$D$5
Cold During April No	34.15	121.85		=(B$5*$D4)/$D$5	=(C$5*$D4)/$D$5
	CHI-SQUARE
	Cold During September Yes	Cold During September No		FORMULA FOR CHI-SQUARE
Cold During April Yes	2.69	0.75		=(B3-B9)^2/B9	=(C3-C9)^2/C9
Cold During April No	0.78	0.22		=(B4-B10)^2/B10	=(C4-C10)^2/C10
Test statistic	4.44	=SUM(B14:C15)
Critical value	3.84	=CHISQ.INV.RT(0.05,1)

H₀: There is difference in cold prevalence during (in September) and outside of cold season (April)

H₁: There is no difference in cold prevalence during (in September) and outside of cold season (April)

Test statistic = 4.44

Degrees of freedom: df = (Rows-1)*(Columns-1) = (2-1)*(2-1) = 1

Level of significance = 0.05

Critical value = CHIHSQ.INV.RT(probability,df) = CHISQ.IN.RT(0.05,1) = 3.84

Since test statistic is greater than critical value, we do not reject the null hypothesis.

So, there is difference in cold prevalence during (in September) and outside of cold season (April).