Grand Strand Family Medical Center is specifically set up totreat minor medical
ID: 2914998 • Letter: G
Question
Grand Strand Family Medical Center is specifically set up totreat minor medical emergencies or visitors to the Myrtle Beacharea. There are two facilities River Area and the other in MurrellsInlet. The Quality Assurance Department wishes to compare the meanwaiting time for patients at the two locations. Samples of thewaiting times, reported in minutes, follow:
Location,
Waiting Time
Little River
31.730
28.8
29.5
22.1
29.47
18.6
32.94
25.2
29.8
26.5
Murrells Inlet
22.93
23.9
26.9
27.2
26.44
25.6
30.61
29.4
23.1
23.1
26.7
22.3
Assume the population standard deviations are not thesame. At the .05 significance level is there a difference in themean waiting time?
Location,
Waiting Time
Little River
31.730
28.8
29.5
22.1
29.47
18.6
32.94
25.2
29.8
26.5
Murrells Inlet
22.93
23.9
26.9
27.2
26.44
25.6
30.61
29.4
23.1
23.1
26.7
22.3
Explanation / Answer
Grand Strand Family Medical Center is specifically set up totreat minor medical emergencies for visitors to the Myrtle Beacharea. There are two facilities, one in Little River Area and theother in Murrells Inlet. The Quality Assurance Department wishes tocompare the mean waiting time for patients at the two locations.Samples of the waiting times, reported in minutes, follow:
Location Waitingtime
LittleRiver 31.73 28.77 29.53 22.08 29.47 18.60 32.94 25.18 29.82 26.49
MurrellsInlet 22.93 23.92 26.92 27.20 26.44 25.62 30.61 29.44 23.09 23.1026.69 22.31
Assume the population standard deviation are not the same. Atthe .05 significance level, is there a difference in mean waitingtime?
H0: There is no difference in the mean waiting times at the twofacilities, that is, m1 = m2 or m1 - m2 = 0
Ha: The mean waiting times at the two facilities are different,that is, m1 m2 or m1 - m2 0
Two-tailed t- test for difference in population means; a = 0.05;DOF = 10 + 12 -2 = 20; Critical t- score = 2.0860
Decision Rule: Reject H0 if the test t- score < -2.0860 or> 2.0860
Little River
Murrel's Inlet
31.73
22.93
28.77
23.92
29.53
26.92
22.08
27.2
29.47
26.44
18.6
25.62
32.94
30.61
25.18
29.44
29.82
23.09
26.49
23.1
26.69
22.31
n =
10
12
x-bar =
27.46
25.69
s =
4.44
2.68
Since 1.1545 < 2.0860, we fail to reject H0
Conclusion: There is no sufficient evidence that themean waiting times at the two facilities are different
Grand Strand Family Medical Center is specifically set up totreat minor medical emergencies for visitors to the Myrtle Beacharea. There are two facilities, one in Little River Area and theother in Murrells Inlet. The Quality Assurance Department wishes tocompare the mean waiting time for patients at the two locations.Samples of the waiting times, reported in minutes, follow:
Location Waitingtime
LittleRiver 31.73 28.77 29.53 22.08 29.47 18.60 32.94 25.18 29.82 26.49
MurrellsInlet 22.93 23.92 26.92 27.20 26.44 25.62 30.61 29.44 23.09 23.1026.69 22.31
Assume the population standard deviation are not the same. Atthe .05 significance level, is there a difference in mean waitingtime?
H0: There is no difference in the mean waiting times at the twofacilities, that is, m1 = m2 or m1 - m2 = 0
Ha: The mean waiting times at the two facilities are different,that is, m1 m2 or m1 - m2 0
Two-tailed t- test for difference in population means; a = 0.05;DOF = 10 + 12 -2 = 20; Critical t- score = 2.0860
Decision Rule: Reject H0 if the test t- score < -2.0860 or> 2.0860
Little River
Murrel's Inlet
31.73
22.93
28.77
23.92
29.53
26.92
22.08
27.2
29.47
26.44
18.6
25.62
32.94
30.61
25.18
29.44
29.82
23.09
26.49
23.1
26.69
22.31
n =
10
12
x-bar =
27.46
25.69
s =
4.44
2.68
Pooled Standard Deviation,S = sqrt [{(n1 - 1) * s1^2 + (n2 - 1) * s2^2}/(n1 + n2 - 2)]
= sqrt [{(10 - 1) * 4.44^2 + (12 - 1) * 2.68^2}/20] = 3.5807 Standard Error, SE = S * sqrt{(n1 + n2)/(n1 n2)}
= 3.5807 * sqrt{(10 + 12)/(10 * 12)}
= 1.5332 t = (x1-bar - x2-bar)/SE
= (27.46 - 25.69)/1.5332
= 1.1545
Since 1.1545 < 2.0860, we fail to reject H0
Conclusion: There is no sufficient evidence that themean waiting times at the two facilities are different
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