Question

Eight breasts of 7− to 8−week old broiler chickens weighing 0.9 to 1.2 kilograms were taken at random from a poultry-processing plant. The concentration of sarcoplasmic protein (mg N/g tissue) in the breast muscles of these specimens were measured before and after they were irradiate with 10 kGy. The data are presented below:

	Sarcoplasmic Protein (mg/g)
Specimen #	Before	After
1	14.6	12.8
2	14.0	13.5
3	13.9	13.6
4	14.3	13.3
5	13.6	13.9
6	13.7	13.9
7	14.1	13.3
8	14.3	13.5

a) (7 points) At the 2.5 percent level, is there a significant decrease in the true mean sarcoplasmic protein after irradiation? State the assumption(s) required for the test.

b) (3 points) Construct a 95% confidence interval for the μdμd.

Answer 1

Step 1:

Ho: ≤ 0

Ha: > 0

Step 2: Paired T test

employee	Before	After	Diff (Bef-after)	Dev (diff - mean)	Sq deviation
1	14.6	12.8	1.8	1.21	1.47
2	14.0	13.5	0.5	-0.09	0.01
3	13.9	13.6	0.3	-0.29	0.08
4	14.3	13.3	1.0	0.41	0.17
5	13.6	13.9	-0.3	-0.89	0.79
6	13.7	13.9	-0.2	-0.79	0.62
7	14.1	13.3	0.8	0.21	0.05
8	14.3	13.5	0.8	0.21	0.05
Total	113	108	4.700	0.0000	3.2288

mean diff = 4.7/ 8 = 0.588

standard dev= s_D

t = 2.447

Step 3:

t critical (right tailed test) = 2.36462425

As the t stat falls in the rejection region, we reject the Null hypothesis.

Hence we have sufficient evidence to believe that there is a significant decrease in the true mean sarcoplasmic protein after irradiation.

(b) Confidence interval

t value = TINV( 0.025, 7) = 2.841

CI = 0.588 +/- 0.682 = -0.094 , 1.270