Question

Data shows the times for carrying out a blood test at Rivervalley Labs

Using Excel Plot a histogram of the data. What type of distribution does the data appear to follow?

Construct and interpret the 95% confidence interval for the population mean time for carrying out a blood test. Assume that the population standard deviation is unknown.

Times for blood tests (minutes)

2.5

4.9

3.6

4.3

1.9

3.4

3.2

4.0

3.1

3.6

3.9

4.4

3.9

3.1

2.7

3.5

3.6

3.7

4.9

3.6

3.8

3.6

2.5

4.0

3.6

4.0

3.2

3.5

2.6

3.7

4.9

4.0

4.2

2.6

4.4

3.5

4.8

5.0

3.5

3.2

3.6

2.6

3.1

5.0

2.0

4.3

5.0

3.9

3.5

5.3

3.5

4.0

4.1

3.7

4.5

3.7

2.8

3.4

2.8

2.5

2.9

2.4

5.0

3.0

4.1

3.6

3.8

3.2

4.3

3.2

3.8

4.1

1.7

4.3

4.7

3.2

3.1

3.6

2.1

3.4

2.1

3.4

3.3

3.8

2.6

2.5

3.0

4.3

3.8

3.4

1.9

3.0

4.5

4.0

4.6

4.6

3.9

1.7

3.9

4.3

Answer 1

Upper Limit	Frequency
0.5	0
1	0
1.5	0
2	5
2.5	7
3	11
3.5	22
4	29
4.5	14
5	11
5.5	1
6	0
6.5	0
7	0

The nature of the histogram suggests that the distribution is bell-shaped and approximately symmetrical. So, a normal distribution assumption may be valid for this distribution.

-----------------------------------

Assume that the data is pasted on Column A of an Excel worksheet.

The sample mean = AVERAGE(A:A) = 3.578
The sample SD = STDEV.S(A:A) = 0.812
Z = NORMSINV(1 - (0.05/2)) = 1.96

Confidence Interval: Sample mean +/- Z*sample SD/sqrt(N)
= 3.578 +/- 1.96*0.812/sqrt(100) = [3.42, 3.74]