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[answered] At a .05 level of significance using the p-value approach,


This is for an Econ Stats class. This is a problem set, with two portions that need Stata SE. Attached are both the stata data file that you will need to use to answer the stata related questions. The rest are problems you do not need to complete with stata. Please show all working out and please do not use excel. Best if handwritten because instructor requires answers to be handwritten and legible.?


e. At a .05 level of significance using the p-value approach, test the above hypotheses.

 

3. In 2012, seventy percent of Canadian households had an internet connection. A

 

sample of 484 households taken in 2013 showed that 75% of them had an internet

 

connection. We are interested in determining whether or not there has been a significant increase in the percentage of the Canadian households that have internet

 

connections.

 

a. State the null and alternative hypotheses to be tested.

 

b. Compute the test statistic.

 

c. The null hypothesis is to be tested at the 5% level of significance. Determine the

 

critical value(s) for this test.

 

d. What do you conclude?

 

4. An official of a large national union claims that the fraction of women in the

 

union is not significantly different from one-half. A sample of union members

 

showed that there were only 168 women among 400 sampled individuals.

 

a. Compute the sample proportion of female union members.

 

b. Using the critical value approach, carry out a test of this statement. Let ? = .05.

 

c. What is the power of this test if p = .49?

 

d. What is the power of this test if p = .45?

 

e. Use Stata to calculate the power of this test for all values of p between .005 and

 

.995, in increments of .01. Display your results graphically as a power curve.1 Provide an interpretation of this graph. You have to submit both a written interpretation

 

and a printout of the graph to get full credit.

 

5. A machine produces pipes used in airplanes. The average length of the pipe is

 

16 inches. The acceptable variance for the length is .3 inches. A sample of 25 pipes

 

was taken. The average length in the sample was 15.95 inches with a variance of .4

 

inches.

 

a. Construct a 95% confidence interval for the population variance.

 

b. State the null and alternative hypotheses to test whether or not the population

 

variance equals .3 inches.

 

1 See p. 5 for a Stata code that provides the solution to this problem. 2 c. Compute the test statistic.

 

d. The null hypothesis is to be tested at the 5% level of significance. State the decision rule for the test using the critical value approach.

 

e. What do you conclude about the population variance?

 

6. A company claims that the standard deviation in their delivery times is less than

 

5 days. A sample of 27 past customers was taken. The average delivery time in

 

the sample was 14 days with a standard deviation of 4.5 days. At the 5% level of

 

significance, test the company?s claim. Use the critical value approach.

 

7. The standard deviation of the ages of a sample of 16 executives from the northern states was 8.2 years; while the standard deviation of the ages of a sample of 26

 

executives from the southern states was 12.8 years. At ? = .1, test to see if there

 

is any difference between the variances of the ages of all the northern and all the

 

southern executives.

 

8. Download PSID70.dta from LATTE. This data set represents a random sample

 

of U.S. individuals in the 1970s and originates from the Panel Study of Income Dynamics (PSID), the longest running longitudinal household survey in the world.

 

For each individual, we observe the values of nine variables: age (Age in years),

 

educ (Years of schooling), black (1 if black, 0 otherwise), hispanic (1 if Hispanic,

 

0 otherwise), married (1 if married, 0 otherwise), nodegree (1 if less than 12 years of

 

schooling, 0 otherwise), re74 (Real earnings in 1974), re75 (Real earnings in 1975),

 

and re78 (Real earnings in 1978). Open this data set in Stata. You have to submit

 

both a written response to the following questions and a printout of the Stata output to get

 

full credit.

 

a. For educ, test the following hypotheses (by typing ttest educ==12):

 

H0 : ? = 12

 

Ha : ? 6= 12

 

Let ? = .05. Report the value of the test statistic, t. Determine the p-value. What

 

do you conclude?

 

b. What do you conclude about the following hypotheses? (Using the same command in Stata, determine the p-value.)

 

H0 : ? ? 12

 

3 Ha : ? > 12

 

c. For re78, test the following hypotheses (by typing ttest re78==22000):

 

H0 : ? ? 22000

 

Ha : ? < 22000

 

Let ? = .05. Report the value of the test statistic, t. Determine the p-value. What

 

do you conclude?

 

d. For hispanic, test the following hypotheses (by typing prtest hispanic==.02):

 

H0 : p ? .02

 

Ha : p > .02

 

Let ? = .05. Report the value of the test statistic, z. Determine the p-value. What

 

do you conclude?

 

e. For hispanic, test the following hypotheses (by typing prtest hispanic==.03):

 

H0 : p ? .03

 

Ha : p > .03

 

Let ? = .05. Report the value of the test statistic, z. Determine the p-value. What

 

do you conclude?

 

f. For educ, test the following hypotheses (by typing sdtest educ==3):2

 

H0 : ?2 = 9

 

Ha : ? 2 6 = 9

 

Let ? = .05. Report the value of the test statistic, ?2 . Determine the p-value. What

 

do you conclude?

 

g. For re74 and re75, test the following hypotheses (by typing sdtest re75==re74):

 

2

 

2

 

H0 : ?re75

 

? ?re74

 

2

 

2

 

Ha : ?re75

 

> ?re74

 

Let ? = .05. Report the value of the test statistic, F. Determine the p-value. What

 

do you conclude?

 

h. For re75 and re78, test the following hypotheses (by typing sdtest re78==re75):

 

2

 

2

 

H0 : ?re78

 

? ?re75

 

2

 

2

 

Ha : ?re78

 

> ?re75

 

Let ? = .05. Report the value of the test statistic, F. Determine the p-value. What

 

do you conclude?

 

2 Note that the syntax of this command requires reporting the hypothesized value of the population standard deviation (instead of variance). Nevertheless, Stata performs the standard test for

 

testing hypotheses about a population variance (based on the chi-squared distribution). 4 Hint for Problem 4e: In your Command window, type doedit to open a text editor

 

that is provided in Stata. In this text editor, retype the following code:3

 

clear all

 

scalar c1 = .5 + invnorm(.025)*sqrt((.5*.5)/400)

 

scalar c2 = .5 + invnorm(.975)*sqrt((.5*.5)/400)

 

postfile union p pow using union, replace

 

forvalues i = .005(.01).995 {

 

scalar z1 = (c1-?i?)/sqrt((?i?*(1-?i?))/400)

 

scalar z2 = (c2-?i?)/sqrt((?i?*(1-?i?))/400)

 

scalar pow = normal(z1) + (1 - normal(z2))

 

post union (?i?) (pow)

 

}

 

postclose union

 

use union, clear

 

twoway (line pow p if p<.5, lc(gs0)) (line pow p if p>.5, lc(gs0)), xline(.5)

 

graph export union.pdf, replace

 

clear all

 

Then, save the resulting text document as union.do in your current (Stata) working directory. Return to the Command window and type do union. This will execute your program for you ? and create two new files in your working directory:

 

union.dta and union.pdf. This latter file will be a graph with your power curve. 3 Note that, for the left single quote, Stata uses the grave accent, which occupies a key by itself

 

on most computer keyboards. On U.S. keyboards, the grave accent is located at the top left, next to

 

the numeral 1. For the right single quote, Stata uses the standard single quote, or apostrophe. On

 

U.S. keyboards, the single quote is located on the same key as the double quote, on the right side

 

of the keyboard next to the Enter key. 5

 


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