Question

1. 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 two places past the decimal in your calculations.

Hours of Sleep per Night

Arts:5,6,8,7,7,6

Sciences:7,5,4,5,8,7

Business:8,7,8,6,5,8

Preliminary Calculations

Arts Sciences Business

Ex	39	36	42
xk	6.5	6	7
xk2	259	228	302
nk	6	6	6

X= 6.50

(P.S.: No need to square the values. Already done in the Preliminary table, so use these values)

Answer 1

Result:

H1: At least one of the mean is different from the others

				Total
Ex	39	36	42	117
xk	6.5	6	7
xk2	259	228	302	789
nk	6	6	6	18

Grand total ==117

T1, T2 , T3 are group totals

=789-117^2/18 =28.5

=39^2/6+36^2/6+42^2/6 - 117^2/18 =3

SSE= SST-SSG    = 28.5-3=25.5

ANOVA table
Source	SS	df	MS	F
Between	3.00	2	1.500	0.88
Error	25.50	15	1.700
Total	28.50	17

At 0.05 level, Table value of F with (DF1=2, DF2=15 ) =3.68

Calculated F=0.88 < 3.68 the table value

The null hypothesis is not rejected.

The data indicate there is no significant difference in hours of sleep per night across Arts, Science, and Business students groups.