Question

In: Statistics and Probability

A fitness trainer is interested in investigating whether ethnicity and the first exercise activity that members...

A fitness trainer is interested in investigating whether ethnicity and the first exercise activity that members engage in are dependent. The table below shows the results of the trainer's observation of randomly selected members. Frequencies of Ethnicity and Exercise Activity Cardio Weight Machines Free Weights White 88 82 88 Hispanic 86 82 95 Black 44 57 63 Other 60 41 48 What can be concluded at the alpha = 0.01 significance level? What is the correct statistical test to use? Homogeneity Independence Goodness-of-Fit Paired t-test What are the null and alternative hypotheses? H_0: The distribution of first exercise activity is the same for each ethnicity. Ethnicity and first exercise activity are independent. Ethnicity and first exercise activity are dependent. The distribution of first exercise activity is not the same for each ethnicity. H_1: Ethnicity and first exercise activity are independent. The distribution of first exercise activity is not the same for each ethnicity. Ethnicity and first exercise activity are dependent. The distribution of first exercise activity is the same for each ethnicity. The test-statistic for this data = (Please show your answer to three decimal places.) The p-value for this sample = (Please show your answer to four decimal places.) The p-value is alpha Based on this, we should accept the null fail to reject the null reject the null Thus, the final conclusion is... There is sufficient evidence to conclude that the distribution of first exercise activity is not the same for each ethnicity. There is sufficient evidence to conclude that ethnicity and first exercise activity are independent. There is insufficient evidence to conclude that the distribution of first exercise activity is not the same for each ethnicity. There is insufficient evidence to conclude that ethnicity and first exercise activity are dependent. There is sufficient evidence to conclude that ethnicity and first exercise activity are dependent.

Solutions

Expert Solution

correct statistical test to use? Independence

Ho:Ethnicity and first exercise activity are independent

H1: Ethnicity and first exercise activity are dependent.

Applying chi square test:

 Expected Ei=row total*column total/grand total cardio weight m/c free weights Total white 86.00 81.05 90.95 258 Hispanic 87.67 82.62 92.71 263 Black 54.67 51.52 57.81 164 other 49.67 46.81 52.53 149 total 278 262 294 834 chi square    χ2 =(Oi-Ei)2/Ei cardio weight m/c free weights Total white 0.0465 0.0111 0.0957 0.153 Hispanic 0.0317 0.0047 0.0565 0.093 Black 2.0813 0.5828 0.4654 3.129 other 2.1499 0.7207 0.3899 3.260 total 4.309 1.319 1.007 6.6360

The test-statistic for this data =6.636

The p-value for this sample = 0.3558

fail to reject the null

There is insufficient evidence to conclude that ethnicity and first exercise activity are dependent

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