Question

Countries	Sample Mean	Sample Standard Deviation	Sample Size
Canada	x1=1.80	s1=0.91	n= 20
Portugal	x2=1.96	s2=1.00	n= 20

Do each of the following.

A) Test at 5% individually for each of the means.

B) Obtain a 95% confidence interval for the difference of means for the two countries.

C) Test an appropriate pair of hypotheses for the two means at 5% level of significance.

Answer 1

(a)

1.800	mean Canada
0.910	std. dev.
0.203	std. error
20	n
19	df
8.846	t
3.65E-08	p-value (two-tailed)

1.9600	mean Portugal
1.0000	std. dev.
0.2236	std. error
20	n
19	df
8.765	t
4.20E-08	p-value (two-tailed)

Both means are statistically significant.

(b) The 95% confidence interval for the difference of means for the two countries is between -0.77204 and 0.45204.

-0.77204	confidence interval 95.% lower
0.45204	confidence interval 95.% upper
0.61204	margin of error

(c) The hypothesis being tested is:

H0: µ1 = µ2

H1: µ1 ≠ µ2

Canada	Portugal
1.8	1.96	mean
0.91	1	std. dev.
20	20	n
	38	df
	-0.16000	difference (Canada - Portugal)
	0.91405	pooled variance
	0.95606	pooled std. dev.
	0.30233	standard error of difference
	0	hypothesized difference
	-0.529	t
	.5997	p-value (two-tailed)

Since the p-value (0.5997) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that there is a difference of means for the two countries.