Question

uppose you want to test the claim the the paired sample data given below come from a population for which the mean difference is μd=0.

x 51 89 60 78 75 81 59

y 79 84 87 75 93 55 64

Use a 0.01 significance level to find the following:

(a) The mean value of the differnces d for the paired sample data d⎯⎯⎯=

(b) The standard deviation of the differences d for the paired sample data sd=

(c) The t test statistic t=

(d) The positive critical value t=

(e) The negative critical value t=

(f) Does the test statistic fall in the critical region? A. Yes B. No

(g) Construct a 99% conficence interval for the population mean of all differences x−y. <μd<

Answer 1

The statistical software output for this problem is:

Summary statistics:

Column	Mean	Std. dev.
Differences	-6.2857143	19.559433

Paired T hypothesis test:
μ_D = μ₁ - μ₂ : Mean of the difference between x and y
H₀ : μ_D = 0
H_A : μ_D ≠ 0
Hypothesis test results:

Difference	Mean	Std. Err.	DF	T-Stat	P-value
x - y	-6.2857143	7.3927709	6	-0.85025147	0.4278

99% confidence interval results:

Difference	Mean	Std. Err.	DF	L. Limit	U. Limit
x - y	-6.2857143	7.3927709	6	-33.693881	21.122453

Hence,

a) Mean = -6.2857

b) Standard deviation = 19.5594

c) Test statistic = -0.8503

d) Positive critical value = 3.7074

e) Negative critical value = -3.7074

f) No

g) 99% confidence interval:

-33.6939 < μd < 21.1225