Question 4 [14 Marks] Many people have high anxiety about visiting the dentist.
ID: 3331104 • Letter: Q
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Question 4 [14 Marks] Many people have high anxiety about visiting the dentist. Researchers want to know if this affects blood pressure in such a way that the mean blood pressure while waiting to see the dentist is higher than it is an hour after the visit. Ten individuals have their systolic blood pressures measured while they are in the dentist’s waiting room and again an hour after the conclusion of the visit to the dentist. The data are as follows:
Person
1
2
3
4
5
6
7
8
9
10
Before:
132
135
149
133
119
121
128
132
119
110
After:
118
137
140
139
107
116
122
124
115
10
a) Is this paired or unpaired data? b) Calculate the summary statistics relevant to this problem. c) Compute a 95% confidence interval for the mean change in systolic blood pressure. Show all your working. d) Based on that confidence interval, is there sufficient evidence to conclude that systolic blood pressure has fallen an hour after the visit? e) The investigators want to estimate the mean change in systolic blood pressure to an accuracy of ± 1.0 mmHg with 95% confidence, using the same measurement process (with a known standard deviation of 5 mmHg). How many people in the sample (independent measurements) would be needed to achieve this?
Person
1
2
3
4
5
6
7
8
9
10
Before:
132
135
149
133
119
121
128
132
119
110
After:
118
137
140
139
107
116
122
124
115
10
Question 4 [14 Marks] Many people have high anxiety about visiting the dentist. Researchers want to know if this affects blood pressure in such a way that the mean blood pressure while waiting to see the dentist is higher than it is an hour after the visit. Ten individuals have their systolic blood pressures measured while they are in the dentist's waiting room and again an hour after the conclusion of the visit to the dentist. The data are as follows: Person1 Before: 132 135 149 133 119 121 128 132 119 110 After 118137 140 139 107 116 122 124 115103 4 a) Is this paired or unpaired data? b) Calculate the summary statistics relevant to this problem c) Compute a 95% confidence interval for the mean change in systolic blood pressure Show all your working d) Based on that confidence interval, is there sufficient evidence to conclude that systolic blood pressure has fallen an hour after the visit? e) The investigators want to estimate the mean change in systolic blood pressure to an accuracy of ± 1.0 mmHg with 95% confidence, using the same measurement process (with a known standard deviation of 5 mmHg). How many people in the sample (independent measurements) would be needed to achieve this?Explanation / Answer
Confidence Interval
CI = d ± t a/2 * (Sd/ Sqrt(n))
Where,
d = di/n
Sd = Sqrt( di^2 – ( di )^2 / n ] / ( n-1 ) )
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
d = ( di/n ) =57/10=5.7
Pooled Sd( Sd )= Sqrt [ 651- (57^2/10 ] / 9 = 6.019
Confidence Interval = [ 5.7 ± t a/2 ( 3.475/ Sqrt ( 10) ) ]
= [ 5.7 - 2.262 * (1.904) , 5.7 + 2.262 * (1.904) ]
= [ 1.394 , 10.006 ]
we have sufficient evidence to conclude that systolic blood pressure has fallen an hour after the visit.
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