Question

You need to find out if location affects death R for viral influenza. You find out the death R for 10 Americans and 10 foriegners:

(a) Infer the mortality rate across everyone has a normal distribution and the variance for americans is equal to the variance for foriegners. Test whether the mean death R in Americans is higher than that in foriegners at a 5% significance level.

(b) In previous question, we assume that the variances of death rates in americans and foreigners are the same. Test whether this inference is ok at a 5% significance level.

americans	Death R	Foriegners	Death R
Person 1	4.1	Person 1	3.4
Person 2	8.6	Person 2	3.9
Person 3	7.2	Person 3	6.4
Person 4	2.2	Person 4	2.5
Person 5	5.1	Person 5	4.1
Person 6	7.4	Person 6	3.1
Person 7	5.3	Person 7	2.5
Person 8	3.2	Person 8	3.6
Person 9	3.1	Person 9	4.6
Person 10	3.5	Person 10	3.0

Answer 1

(a) Infer the mortality rate across everyone has a normal distribution and the variance for americans is equal to the variance for foriegners. Test whether the mean death R in Americans is higher than that in foriegners at a 5% significance level.

The hypothesis being tested is:

H0: µ1 = µ2

H1: µ1 > µ2

The p-value is 0.0598.

Since the p-value (0.0598) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that the mean death R in Americans is higher than that in foreigners.

(b) In previous question, we assume that the variances of death rates in americans and foreigners are the same. Test whether this inference is ok at a 5% significance level.

σ₁: standard deviation of americans

σ₂: standard deviation of Foriegners

Ratio: σ₁/σ₂

F method was used. This method is accurate for normal data only.

Descriptive Statistics

Variable	N	StDev	Variance	95% CI for σ²
americans	10	2.145	4.600	(2.176, 15.331)
Foriegners	10	1.161	1.348	(0.638, 4.492)

Ratio of Variances

Estimated Ratio	95% CI for Ratio using F
3.41339	(0.848, 13.742)

The hypothesis being tested is:

Null hypothesis	H₀: σ₁² / σ₂² = 1
Alternative hypothesis	H₁: σ₁² / σ₂² ≠ 1
Significance level	α = 0.05

Method	Test Statistic	DF1	DF2	P-Value
F	3.41	9	9	0.082

The p-value is 0.082.

Since the p-value (0.082) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that the variances of death rates in americans and foreigners are the same.