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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