Question

3.4 - Two laboratory procedures for determining the amylase level in human body fluids are compared. The new

method is less expensive than the existing method, but may give different results. To compare, both methods

are used on each of 10 subjects, with the following results (amylase level in units per millilitre):

Subject	Existing method	New method
1	38	46
2	48	57
3	58	73
4	53	60
5	75	86
6	58	67
7	59	65
8	46	58
9	69	85
10	59	74

a) Explain why the results should be analysed as paired data.

b) Do the methods significantly for the level of amylase determined?

Carry out a hypothesis test (including all the steps) and write your conclusion in plain English. Use a significance level of 10%.

c) Calculate a 90% confidence interval for the difference in amylase level for the two methods. Based on your hypothesis test result, did you expect to find 0 in the interval? Explain

(Show all working out and dont use technology (ie. spss or excel))

Answer 1

(a) The results should be analyzed as paired data because the 2 samples: Existing method and New Method are not independent. They are correlated pairs. The same subject is measured twice.

(b)

From the given data,values of d = Existing Method - New Method are got as follows:

d = Existing Method - New Method = - 8, - 9, - 15, - 7, - 11, -9, - 6, - 12, - 16, - 15

From the d values, the following statistics are calculated:

n = 10

= - 108/10 = - 10.8

s_d = 3.5839

SE= s_d/

= 3.5839/

1.1333

Test statistic is given by:

t = - 10.8/1.1333

= - 9.5295

= 0.10

ndf = 10 - 1 = 9

From Table,critical values of t = 1.8331

Since the calculated value of t = - 9.5295 is less than critical value of t = - 1.8331, the difference is significant. Reject null hypothesis.

Conclusion:

The data support the claim that both methods determine the level of armylase significantly differently.

(c)

Confidence Interval:

- 10.8 (1.8331 X 1.1333)

= 10.8 2.0775

= ( - 12.8775 ,- 7.9225)

So,

Confidence Interval:

- 12.8775 < < - 7.9225

(d)

Based on our hypothesis test result, we did not expect to   find 0 in the interval.

Explanation: The result of the Hypothesis test is both methods determine the level of armylase significantly differently.. The confidence interval thus does not contain 0.