A university department is deciding which of the research proposals to support. Eight members of staff...

A university department is deciding which of the research proposals to support. Eight members of staff were asked to read the proposals and to award each of them a mark out of 100. Following are the marks awarded to the proposals.

Staff	Proposal 1	Proposal 2
1	53	75
2	46	67
3	60	69
4	53	51
5	66	76
6	59	59
7	52	65
8	67	68

Determine a 95% confidence interval for the difference in the mean marks awarded to the two proposals.

Solutions

Expert Solution

since sample subject is used in both groups, we will use paired t test

for 95% CI; and 7 degree of freedom, value of t=	2.365
therefore confidence interval=sample mean -/+ t*std error
margin of errror =t*std error=	7.712195
lower confidence limit =	-16.96
upper confidence limit =	-1.54
from above 95% confidence interval for mean difference in the mean marks awarded =(-16.96 to -1.54)

orchestra answered 1 year ago

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