It is known that life expectancy (population mean age at death) of males in urba

ID: 3393397 • Letter: I

Question

It is known that life expectancy (population mean age at death) of males in urban areas of a less developed country is 55 years. A demographer suspects that life expectancy in rural areas of this country is less than 55 years. She identifies a random sample of 196 recent deaths of males in rural areas. In this sample, the mean age at death is 51.5 years, and the standard deviation of ages at death is 21 years. (This problem does not reflect the actuarial definition of life expectancy, which is the expected number of years until death, computed at birth, using the age-specific mortality rates prevailing at the time of birth.) Which are the appropriate null and alternative hypotheses? H_0 : mu = 55 vs. H_A : mu 55 H_0 : mu > 55 vs. H_A : mu 55 what test statistic should we use? what is the form of the rejection region? Reject Ho if X cv. Reject Ho if X CV_2. Accept H_0 What is the conclusion of the test? (Use a 10% significance level.) Reject H_0 in favor of H_a

Explanation / Answer

Q9.

Q10.

answer a

a). t test

t = rac { (ar x - mu)} {rac {s} {sqrt{n}}}

Q11.

Answer b

b). Reject Ho if X > cv

Q12).

Answer b

b). Reject Ho in favor of HA

t Test for Hypothesis of the Mean

Data

Null Hypothesis m=

Level of Significance

0.1

Sample Size

196

Sample Mean

51.5

Sample Standard Deviation

Intermediate Calculations

Standard Error of the Mean

1.5000

Degrees of Freedom

195

t Test Statistic

-2.3333

Lower-Tail Test

Lower Critical Value

-1.2859

p-Value

0.0103

Reject the null hypothesis