Question

# You wish to determine if there is a linear correlation between the two variables at a...

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?
rc.v. =

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

• 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!

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.