Question

It is known that in Canada females live longer than males, on average. The Insurance company is trying to estimate the difference for various social groups in different parts of Canada. Two random samples were taken in Ontario, providing life expectancy data at 65 for males and females who worked in Business (see the data file). Use t-test for two means as both distributions are approximately normal. Test the claim that the females live longer than males on average. Provide Excel output.

a. Write the null and alternative hypotheses for this test.

b. Do you think we should use t-test for equal or unequal variances? What is the value of the t-test statistic?

c. What is the associated P-value?

d. State the conclusion using α = 0.05. Do it using both P-value and critical value.

e. Please reconsider the previous question at α = 0.01. Is your conclusion different? Why?

Data:

	Female Life Expectancy	Male Life Expectancy
1	23.45	20.98
2	24.11	21.25
3	23.48	13.55
4	25.12	17.19
5	24.91	14.45
6	23.32	20.27
7	23.23	21.29
8	21.05	22.45
9	23.65	16.65
10	24.40	18.27
11	23.05	13.53
12	23.37	15.59
13	24.92	22.12
14	22.27	14.20
15	22.05	15.43
16	24.49	23.36
17	23.30	25.32
18	23.96	18.52
19	24.05	14.21
20	23.08	20.26
21	22.56	18.76
22	22.85	21.11
23	24.45	19.97
24	22.65	20.51
25	23.37	22.30
26	23.05	23.98
27	23.37	21.74
28	24.92	21.18
29	22.27	22.82
30	22.05	17.93
31		19.40
32		24.60
33		14.20
34		19.00
35		19.80

Answer 1

(a)

Sample 1 = Female

Sample 2 = Male

Hypotheses are:

(b)

Since it is not given that population variances are equal so we should use independent sample t test-unequal variance.

Following is the output of t test generated by excel:

The test statistics is

t = 6.91

(c)

The p-value is : 0.0000

(d)

Since p-value is less than 0.05 so we reject the null hypothesis. There is evidence to conclude that the females live longer than males on average.

-------------------------

Test is right tailed so critical value of t for df=40 and alpha=0.05 using excel function "=TINV(0.1,40)" is 1.684.

Since t > 1.684 so we reject the null hypothesis. There is evidence to conclude that the females live longer than males on average.

(e)

Since p-value is less than 0.01 so we reject the null hypothesis. There is evidence to conclude that the females live longer than males on average.