Question

The current answers I have are incorrect so if the multiple choice and everything in blue can be solved that would be great! thank you!

An industry study was recently conducted in which the sample correlation between units sold and marketing expenses was 0.74. The sample size for the study included 17 companies Based on the sample results, test to determine whether there is a significant positive correlation between these two variables. Use α =0.10 Click the icon to view the t-distribution table What are the appropriate null and alternative hypotheses to test for a positive correlation? OF. Ho: p20 Calculate the t-test statistic for correlation 30792 (Round to four decimal places as needed.) Determine the critical value(s) for the rejection region for the test statistic t. Select the correct choice below and fill in the answer box to complete your choice. (Round to four decimal places as needed.) . c 0.005 = ± 2.9208 Since the test statistic is in the rejectionegion reject the null hypothesis. The data do support the contention that there is a correlation between units sold and marketing expenses

Answer 1

We have to test, H0: $\rho$ $\leq$ 0 against HA: $\rho$ > 0.

Hence, Option (A) is the correct choice. (Ans).

The test-statistic is, T = $\frac{r\sqrt{n-2}}{\sqrt{1-r^2}}$ , where, r = 0.74, n = 17

Thus, T = 4.2610. (Ans).

T ~ t-distribution with (n-1) i.e. 16 d.f. under H0.

The critical value for the rejection region = = $t_{0.99,16}$ = 2.583. (Ans).

We reject H0, if observed T > 2.583.

Since, the test-statistic is in the rejection region, we reject the null hypothesis. The data does support the contention that there is a correlation between units sold and marketing expenses. (Ans).