Question

You wish to determine if there is a linear correlation between the two variables at a significance level of α=0.01. You have the following bivariate data set.

x	y
8.8	46.6
30.2	68.7
42.7	61.8
30.8	83.1
27.3	45.1
26.9	46.1
32	110.2
9.2	25.9
18.4	102.7
42	51.8
10.4	86.1
46.3	41.1
12.7	42.9
19.6	27.3
22.9	59.5
26.9	59.7
2.4	46.8

What is the critical value for this hypothesis test?
r_c.v. =  

What is the correlation coefficient for this data set?
r =  

Your final conclusion is that...

• There is insufficient sample evidence to support the claim the there is a correlation between the two variables.
• There is sufficient sample evidence to support the claim that there is a statistically significant correlation between the two variables.

Note: Round to three decimal places when necessary.

Please show how to solve with a TI-84 calculator. This is the only way I can solve. Thank you!

Answer 1

Level of significance = 0.01

Sample size = n = 17

Degrees of freedom = n - 2 = 17 - 2 = 15

Critical value = c.v = 0.606

Now we have to find the correlation coefficient (r)

By using TI-84 calculator we have to find correlation coefficient.

Click on STAT -------> Edit -------> Enter x values into L1 and y values into L2.

Then click 2ND -------> 0 ( Zero) ---------> DiagnosticOn ------->Enter

Then click on STAT ---------> CALC --------> LinReg( a + bx) -------->

Xlist: L1

Ylist: L2

FreqList:

Store RegEQ:

Calculate

We get

The correlation coefficient = r = 0.1463

Critical value > r we fail to reject null hypothesis.

Conclusion:

• There is insufficient sample evidence to support the claim the there is a correlation between the two variables.