The number of hours 10 students spent studying for a test and their scores on th

Question

The number of hours 10 students spent studying for a test and their scores on that test are shown in the table. Is there enough evidence to conclude that there is a significant linear correlation between the data? Use alpha = 0.01. Setup the hypothesis for the test. H_0: rho 0 H_a: rho 0 Identify the critical value(s). Select the correct choice below and fill in any answer boxes within your choice. (Round to three decimal places as needed.) A. The critical values are -t_0 = and t_0 = B. The critical value is Calculate the test statistic. t = (Round to three decimal places as needed.) What is your conclusion? There enough evidence at the 1% level of significance to conclude that there a significant linear correlation between hours spent studying and test score.

Explanation / Answer

Null hypothesis H0: = 0
Alternative hypothesis HA: 0

Here degrees of freedom = n - 2 = 10 - 2 = 8

Using standard t-table, critical values for alpha = 0.01 are -t0 = -3.3554 and t0 = 3.3554. Here we have two critical values as this is a two tailed test.

Test statistics t = r*sqrt(n-2)/sqrt(1 - r^2)

Here value of r = 0.9566 (this value is found using excel regression analysis)

t = 0.9566*sqrt(10 - 2)/sqrt(1 - 0.9566^2) = 9.285

As value of test statistics is greater than critical value, we reject the null hypothesis.

There is enough evidence at the 1% level of significance to conclude that there is a significant linear correlation between hours spent studing and test score.

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