Testing the Spearman Rank Correlation Coefficient for n30 ...

Question

Testing the Spearman Rank Correlation Coefficient for n>30 When you are testing the significance of the Spearman rank correlation coefficient and the sample size n is greater than 30, you can use the expression below to find the critical value.

Formula for calculating the critical value of the Spearman rank correlation coefficient for large sample sizes.

In Exercises 13 and 14, test the Spearman rank correlation coefficient

[APPLET] Work Injuries The table shows the average hours worked per week and the numbers of on-the-job injuries for a random sample of U.S. companies in a recent year. At α = =0.10, can you conclude that there is a significant correlation between average hours worked and the number of on-the-job injuries?

Table displaying average hours worked and corresponding on-the-job injuries for U.S. companies in a recent study.

Accepted Answer

All right. Hello, everyone. So, this question says, a researcher collects data on the number of hours spent exercising per week and cholesterol levels for a random sample of 35 adults. The Spearman rank correlation coefficient calculated from the data is RS equals -0.38. At alpha equals 0.10, is there a significant correlation between hours of exercise and cholesterol levels? Use a two-tailed test. And here we have 4 different answer choices labeled A through D. So first, let's point out the information that we know. We know that N is equal to 35, R S is equal to -0.38. And alpha equals 0.10. So using this information, we can find a test statistic Z, which we can then compare to a critical value. So recall it Z. Is equal to RS multiplied by the square root of and subtracted by 2. And divided by 1 subtracted by R S squared. So, plugging in the information that you have, Z is equal to 0.38. Multiplied by the square root of 35 subtracted by 2. Divided by one subtracted by. -0.38. Squared So, evaluating this expression ultimately gives you a Z value or a test statistic equal to -2.3598. And now you're left to find the critical value or a two-tailed test. And so that critical value for a two-tilt test at alpha equals 0.10 is positive and negative 1.645. So, for the final step of this problem, let's round our test statistic to 2.360. And so to make a comparison, we have to know the absolute value of our test statistic. So, what's worth mentioning is that the absolute value of -2.360. Is greater than 1.645. Because of this, because it's greater than. The larger of the two critical values. It is within the rejection region, which means that we can reject the null hypothesis. So rejecting the null hypothesis in this context would prove that there is a significant correlation between Exercise and cholesterol levels. However, the negative correlation. Indicates that whereas one increases, the other decreases. So in this case, as the amount of exercise increases, the cholesterol level decreases. But in any case, our correct answer is going to be option A, which reads, yes, there is a significant correlation. And there you have it. So with that being said, thank you so very much for watching, and I hope you found this helpful.

Key Concepts

Spearman Rank Correlation Coefficient

Critical Value

Significance Level (α)

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