Question

A recent study1 investigates the effectiveness of different types of face coverings in restricting the distance of respiratory droplets caused by coughing. Using a series of simulated coughs through a mannequin, the researchers gathered the following data:

	means of droplet distance (inches)	sample variances of droplet distance (inches)	sample size
Uncovered	96	900	5
Bandana	43	400	5
Folded Hankerchief	15	100	5
Stitched Mask	2.5	5	5
Overall	39.125

Using ANOVA, setup and evaluate a hypothesis test where the null hypothesis is that the population mean of droplet distance is the same regardless of face covering at ? = 0.01. (24 points)

Answer 1

The hypothesis being tested is:

H₀: µ₁ = µ₂ = µ₃ = µ₄

H_a: At least one means is not equal

	x	s²	n	n*(x - xgrand)²	(n - 1)*s²
Uncovered	96	900	5	16173.83	3600
Bandana	43	400	5	75.07813	1600
Folded Hankerchief	15	100	5	2910.078	400
Stitched Mask	2.5	5	5	6706.953	20
xgrand	39.125			SSB	SSE
				25865.94	5620
Source	SS	df	MS	F	p-value
Between	25865.94	3	8621.979	24.54656	0.0000
Error	5620	16	351.25
Total	31485.94	19

The p-value is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.01), we can reject the null hypothesis.

Therefore, we cannot conclude that the population mean of droplet distance is the same regardless of face covering.

Please give me a thumbs-up if this helps you out. Thank you!