d. The p-value for this sample(Please show your answer to four decimal places.)%3De. The p-value is Select an answerf. Based on this, we shouldO accept the nullO reject the nullO fail to reject the nullg. Thus, the final conclusion is...O There is sufficient evidence to conclude that the distribution of first exercise activity is notthe same for each ethnicity.O There is insufficient evidence to conclude that the distribution of first exercise activity is notthe same for each ethnicity.O There is sufficient evidence to conclude that ethnicity and first exercise activity areindependent.OThere is sufficient evidence to conclude that ethnicity and first exercise activity aredependent.O There is insufficient evidence to conclude that ethnicity and first exercise activity aredependent. A fitness trainer is interested in investigating whether ethnicity and the first exercise activitythat members engage in are dependent. The table below shows the results of the trainer's observation ofrandomly selected members.Frequencies of Ethnicity and Exercise ActivityWeight Machines8085CardioFree WeightsWhite8482100HispanicBlackOther5450485570What can be concluded at the a 0.01 significance level?a. What is the correct statistical test to use?O HomogeneityO Paired t-testO Goodness-of-FitO Independenceb. What are the null and alternative hypotheses?HoEthnicity and first exercise activity are independent.O The distribution of first exercise activity is not the same for each ethnicity.O The distribution of first exercise activity is the same for each ethnicity.O Ethnicity and first exercise activity are dependent.HEO The distribution of first exercise activity is the same for each ethnicity.Ethnicity and first exercise activity are dependent.Ethnicity and first exercise activity are independent.OThe distribution of first exercise activity is not the same for each ethnicity.(Please show your answer to three decimal places.)c. The test-statistic for this data =(Please show your answer to four decimal places.)d. The p-value for this sample =288

The study is about investigating whether ethnicity and the first exercise activity that members engage in are dependent.a. Since the test about dependent or not indicating that the correct statistically test to use is chi-square independence test. Correct Answer: Independence.b. The hypothesis is, Null hypothesis: H0: Ethnicity and first exercise activity are independent. Alternative hypothesis: H1: Ethnicity and first exercise activity are dependent.c. The expected counts formula is, Expected count=Row totalColumn totalGrand total The expected counts are, Cardio Weight Machines Free Weights Total White 82.3095 81.6998 99.9908 264 Hispanic 80.7506 80.1524 98.0970 259 Black 53.6259 53.2286 65.1455 172 Other 53.3141 52.9192 64.7667 171 Total 270 268 328 866 The value of contribution are, O-E2E Cardio Weight Machines Free Weights White 0.0347 0.0354 0.0000 Hispanic 0.0193 0.2932 0.3789 Black 0.0026 0.5136 0.3617 Other 0.2060 0.0818 0.0235 The test statistic is, χ2=∑O-E2E=0.0347+0.0354+0.0000+0.0193+0.2932+0.3789+0.0026+0.5136+0.3617+0.2060+0.0818+0.0235=1.9508 Thus, the test statistic for this data is 1.951.d. The degrees of freedom is, df=r-1c-1=4-13-1=6 Computation of P-value: The p-value of χ2-distribution for test statistic 1.9508 at 6 degrees of freedom can be obtained using the excel formula “=CHISQ.DIST.RT(1.9508, 6)”. The p-value is 0.9242. Thus, the p-value for this sample is 0.9242.e & f. Decision rule: If p-value ≤ α, then reject the null hypothesis. Decision: The p-value (=0.9242) is greater than the level of significance (=0.01). Based on decision rule, fail to reject the null hypothesis. g. Thus, the final conclusion is there is insufficient evidence to conclude that ethnicity and first exercise activity are dependent.