Question

Researchers surveyed a random sample of 18 students representing three different programs of study to determine whether students get enough sleep each night. Are the differences in hours of sleep per night across Arts, Science, and Business students statistically significant? Conduct a hypothesis test to see. Follow the five-step model with an alpha level of 0.05. Make sure to go through each step and interpret the results in terms of the research question above. Round to twoplaces past the decimal in your calculations.

Hours of Sleep per Night					Preliminary Calculations
Arts	Sciences	Business			Arts	Sciences		Business
5	7	8		Ex	39	36		42
6	5	7		xk	6.5	6		7
8	4	8		Exk(squared)	259	228		302
7	5	6		nk	6	6		6
7	8	5
6	7	8

No need to square the values. Already done in the Preliminary table, so use these values

Answer 1

The hypothesis being tested is:

H0: µ1 = µ2 = µ3

Ha: Not all means are not equal

Arts	Sciences	Business
5	7	8
6	5	7
8	4	8
7	5	6
7	8	5
6	7	8
	Mean	n	Std. Dev
	6.5	6	1.05	Arts
	6.0	6	1.55	Sciences
	7.0	6	1.26	Business
	6.5	18	1.29	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatment	3.00	2	1.500	0.88	.4342
Error	25.50	15	1.700
Total	28.50	17

The p-value is 0.4342.

Since the p-value (0.4342) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we cannot conclude that there is a difference in hours of sleep per night across the groups.