Question

Given the simple regression model Y= βo+ β1X and the regression results that​ follow, test the null hypothesis that the slope coefficient is 0 versus the alternative hypothesis of greater than zero using probability of Type I error equal to 0.10 , and determine the​ two-sided 95% and 99​% confidence intervals.

a. A random sample of size = 36 with b1 = 7 and sb1 =1.7

b. A random sample of size n = 50 with b1= 7.3and sb1= 1.7

c. A random sample of size n = 36 with b1= 5.1 and sb1= 0.88

d. A random sample of size n= 25 with b1=9.4 and sb1= 0.8

a. Test the null hypothesis that the slope coefficient is 0 versus the alternative hypothesis of greater than zero using probability of Type I error equal to 0.10

Reject or do not reject ??? H0. There is sufficient or insufficient ? evidence that the slope coefficient is greater than zero.

Determine the​ two-sided 95​% confidence interval.

​(_________, _________)

​(Round to two decimal places as​ needed.)

Determine the​ two-sided 99​% confidence interval.

​(______​,_______)

​(Round to two decimal places as​ needed.)

b. Test the null hypothesis that the slope coefficient is 0 versus the alternative hypothesis of greater than zero using probability of Type I error equal to 0.10

Do not reject or Reject ??? H0. There is insufficient or sufficient ???? evidence that the slope coefficient is greater than zero.

Determine the​ two-sided 95​% confidence interval.

​(_______​,_______)

​(Round to two decimal places as​ needed.)

Determine the​ two-sided 99​%

confidence interval.

​(_____,_______​)

​(Round to two decimal places as​ needed.)

c. Test the null hypothesis that the slope coefficient is 0 versus the alternative hypothesis of greater than zero using probability of Type I error equal to 0.10.

Reject or Do not reject ????? H0. There is sufficient or insufficient ???? evidence that the slope coefficient is greater than zero.

Determine the​ two-sided 95​% confidence interval.

​(______,_______​)

​(Round to two decimal places as​ needed.)

Determine the​ two-sided 99​% confidence interval.

​(_____​,______​)

​(Round to two decimal places as​ needed.)

d. Test the null hypothesis that the slope coefficient is 0 versus the alternative hypothesis of greater than zero using probability of Type I error equal to 0.10

Reject or Do not reject ???? H0. There is insufficient or sufficient ???? evidence that the slope coefficient is greater than zero.

Determine the​ two-sided 95​% confidence interval.

​(______​,______)

​(Round to two decimal places as​ needed.)

Determine the​ two-sided 99​% confidence interval.

​(______,_____​)

​(Round to two decimal places as​ needed.)

Answer 1

SOLUTION a). A random sample of size = 36 with b1 = 7 and sb1 =1.7

i) NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS Ha:

Type I error or level of significance or alpha=0.1

test statistic= b1/sb1

= 7/1.7

t= 4.12

n= 36

degrees of freedom= n-2=36-2=34

t critical value= 1.31

Since t critical SMALLER than the t cal therefore REJECT NULL HYPOTHESIS H0.

There is sufficient evidence that the slope coefficient is greater than zero.

ii) 95% confidence interval

t critical= 2.03 by using t table

95% confidence interval is ( 3.55,10.45)

iii) 99% confidence interval

99% confidence interval is ( 2.36,11.64)

I have done the first part please re post the rest. Thank You.