Q1 The correlation between two variables is 08 for a sample

Q1- The correlation between two variables is +0.8 for a sample of 10 observations. We wish to show there is a positive relationship between the two variables. Which of the following is a correct statement of the null hypothesis and the alternate hypothesis (H0 = null hypothesis and Ha = alternative hypothesis)?
A.H0: p = 0, HA: p > 0   
B.H0: p = 0, HA: p is not equal to 0   
C.H0: p = 0, HA: p < 0   
D.Depends on the level of significance   

Q2 If we increase the confidence level
A.Confidence interval will also increase.   
B.Confidence interval will not change.   
C.Confidence interval will decrease.   
D.None of the above.

Q3 If we increase the sample size
A.Confidence interval will also increase.   
B.Confidence interval will not change.   
C.Confidence interval will decrease.   
D.None of the above.

The null hypothesis of

Solution

(1) A.H0: p = 0, HA: p > 0 (because we want to test if there is a positive relationship)

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(2)A.Confidence interval will also increase.

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(3)C.Confidence interval will decrease. (the formula for the confidence interval is xbar +/- Z*s/vn)

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(4) The degree of freedom =n-1=25-1=24

It is a two-tailed test.

Given a=0.05, the critical values are t(0.025, df=24) =-2.06 or 2.06 (from student t table)

The rejection regions are if t<-2.06 or t>2.06, we reject the null hypothesis.

Since t= 1.67 is between -2.06 and 2.06, we do not reject the null hypothesis.

Answer: A.average GPA of students is 3.2