The coach of the bombers basketball team is concerned that the controlled by the

Question

The coach of the bombers basketball team is concerned that the controlled by the other team more often than not. The coach decides to randomly select 10 prior games and wants to test, at the 5% significance level, whether the number of points the bombers score is correlated with the number of points their opponents score. State your conclusion to the hypothesis test. a) There is sufficient sample evidence at the 5% significance level to conclude that there is no correlation between the number of points scored by the bombers and their opponents. b) There is sufficient sample evidence at the 5% significance level to conclude that there is some correlation between the number of points scored by the bombers and their opponents. c) There is not sufficient sample evidence at the 5% significance level to conclude that there is no correlation between the number of points scored by the bombers and their opponents. d) There is not sufficient sample evidence at the 5% significance level to conclude that there is some correlation between the number of points scored by the bombers and their opponents.

Explanation / Answer

Solution:

Here, we have to check whether the correlation or linear relationship between the two variables bombers ranks and opponents rank is statistically significant or not. For checking this hypothesis we have to use t test for the population correlation coefficient. The null and alternative hypotheses for this test are given as below:

Null hypothesis: H0: There is statistically significant correlation exists between the two variables bombers ranks and opponents rank.

Alternative hypothesis: Ha: There is no any statistically significant correlation exists between the two variables bombers ranks and opponents rank.

H0: = 0 Versus Ha: 0

This is a two tailed test.

From the given data, we have

Sample correlation coefficient = r = 0.821969

Sample size = n = 10

Degrees of freedom = n – 2 = 10 – 2 = 8

Level of significance = = 0.05

The test statistic formula for this test is given as below:

Test statistic = t = r*sqrt[(n – 2)/(1 – r2)]

Test statistic = t = 0.821969*sqrt[(10 - 2)/(1 – 0.821969^2)]

Test statistic = t = 4.082092

Critical values = -2.3060 and 2.3060

P-value = 0.0035

P-value <

So, we reject the null hypothesis that there is no any statistically significant relationship exists between two variables.

There is sufficient sample evidence at the 5% significance level to conclude that there is some correlation between the number of points scored by the bombers and their opponents.

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