To investigate the tradeoff between time to work and time to sleep, thefollowing equation is estimated:sleep 3,600+0.128totwrk -10.08educ+2.10age6.(112.14) (0.016)n 700, R2 0.102Standard errors are in the parentheses(1) Is either educ or age individually significant at the 5% level? Show yourwork(4.58)(1.35)(2) Dropping educ and age from the equation givessleep 3,780-0.104totwrk(52.04) (0.012)700, R2 0.099nAre educ and age jointly significant in the original equation at the 5% level?Justify your answer

Question
Asked Nov 30, 2019
242 views
To investigate the tradeoff between time to work and time to sleep, the
following equation is estimated:
sleep 3,600+0.128totwrk -10.08educ+2.10age
6.
(112.14) (0.016)
n 700, R2 0.102
Standard errors are in the parentheses
(1) Is either educ or age individually significant at the 5% level? Show your
work
(4.58)
(1.35)
(2) Dropping educ and age from the equation gives
sleep 3,780-0.104totwrk
(52.04) (0.012)
700, R2 0.099
n
Are educ and age jointly significant in the original equation at the 5% level?
Justify your answer
help_outline

Image Transcriptionclose

To investigate the tradeoff between time to work and time to sleep, the following equation is estimated: sleep 3,600+0.128totwrk -10.08educ+2.10age 6. (112.14) (0.016) n 700, R2 0.102 Standard errors are in the parentheses (1) Is either educ or age individually significant at the 5% level? Show your work (4.58) (1.35) (2) Dropping educ and age from the equation gives sleep 3,780-0.104totwrk (52.04) (0.012) 700, R2 0.099 n Are educ and age jointly significant in the original equation at the 5% level? Justify your answer

fullscreen
check_circle

Expert Answer

Step 1

6

 

1.

 

Testing for independent variable “educ”:

 

State the null and alternative Hypotheses:

 

Null Hypothesis:

 

H0: The variable “educ” is not significant.

 

Alternative Hypothesis:

 

H1: The variable “educ” is significant.

 

From the given information, the coefficient of  “educ” is -10.08 and the corresponding standard error is 4.58. The sample size is 700.

 

The test statistic is 2.2009 and it is calculated below:

help_outline

Image Transcriptionclose

Coefficient Standard Error -10.08 4.58 --2.2009

fullscreen
Step 2

The number of sample observations is n=700 and consider the level of significance as 0.05.

The degree of freedom is, – 1 = 700–1 = 699.

Here, the tail of the test is two tail test.

 

The p-value is 0.0281 and it is by Excel function “=T.DIST.2T(2.2009,699)”.

 

Rejection Rule:

 

If p-value ≤ α, then reject the null hypothesis.

If p-value > α, then do not reject the null hypothesis.

 

Conclusion:

 

The p-value is 0.0281 and the level of significance is 0.05.

Here, the p-value is lesser than the level of significance.

From the rejection rule,  reject the null hypothesis.

That is, the variable “educ” is significant.

 

Step 3

Testing for independent variable “age”:

 

State the null and alternative Hypotheses:

 

Null Hypothesis:

 

H0: The variable “age” is not significant.

 

Alternative Hypothesis:

 

H1: The variable “age” is significant.

 

From the given information, the coefficient of  ...

help_outline

Image Transcriptionclose

Coefficient Standard Error 2.10 1.35 =1.5556

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Statistics

Other

Related Statistics Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: The combined SAT scores for the students at a local high school are normally distributed with a mean...

A: The following information has been provided:

question_answer

Q: Views on the Death Penalty. The Pew Research group conducted a poll in which they asked," are you in...

A: The appropriate null and alternative hypotheses are shown below:H0: p1 = p2.Ha: p1 ≠ p2.The test sta...

question_answer

Q: estimate P(at least 8) with n- 13 and p-06 by using the non a 5, is not suitablo on as an approsimal...

A: Checking conditions of np>5 and nq>5:Here, n is 13; p is 0.6.The standard deviation of the pop...

question_answer

Q: A researcher computed a 90% confidence interval for the proportion of students who smoke. If the res...

A: False. Relationship between confidence level and error:The error value increases when the confidence...

question_answer

Q: Ciestion Help If np 25 and nq 25, estimate P(fewer than 7) with n 14 and p 0.5 by using the normal d...

A: Introduction:Denote X as the variable of interest. The exact distribution of X is binomial with n = ...

question_answer

Q: A lightbulb is advertised as lasting 1000 hours with a standard deviation of 150 hours. Assume the l...

A: The lasting duration of lightbulb is normally distributed with mean 1000 hours and standard deviatio...

question_answer

Q: ONLY THE QUESTIONS THAT ARE NOT ANSWERED ! THANK YOU !!!!!

A: According to the provided data,

question_answer

Q: A study of bone density on 5 random women at a hospital produced the following results. A...

A: Step-by-step procedure to obtain the correlation coefficient using Excel-Mega Stat is given below:En...

question_answer

Q: The average cost of tuition and room and board at a small private liberal arts college is reported t...

A: The provided information are: