10. [-15.39 Points] DETAILS BBUNDERSTAT12 10.2.011.M|.S. MY NOTES ASK YOUR TEACHER The Fish and Game Department stocked a lake with sh in the following proportions: 30% catsh, 15% bass, 40% bluegill, and 15% pike. Five years later it sampled the lake to see if the distribution of sh had changed. It found that the 500 sh in the sample were distributed as follows. Catsh Ball Bluegill Pike 122 93 218 57 [0 USE SALT In the 5-year interval, did the distribution of sh change at the 0.05 level? (a) What is the level of signicance? E State the null and alternate hypotheses. o: The distributions are the same. H1: The distributions are different. 0 H0: The distributions are different. H1: The distributions are different. 0 Ho: The distributions are different. H1: The distributions are the same. 0 Ho: The distributions are the same. H1: The distributions are the same. (b) Find the value of the chi-square statistic for the sample. (Round your answer to three decimal places.) Q Are all the expected frequencies greater than 5? 0 Yes ONo What sampling distribution will you use? 0 uniform 0 normal 0 binomial O chi-square O Student's t What are the degrees of freedom? E (c) Estimate the P-value of the sample test statistic. O P-value > 0.100 O 0.050 a, we fail to reject the null hypothesis. O Since the P-value > a, we reject the null hypothesis. O Since the P-value s a, we reject the null hypothesis. O Since the P-value s a, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. O At the 5% level of significance, the evidence is insufficient to conclude that current fish distribution is different than that of five years ago. O At the 5% level of significance, the evidence is sufficient to conclude that current fish distribution is different than that of five years ago