10-10

10. [-/5.39 Points] DETAILS BBUNDERSTAT12 10.2.011.MI.S. MY NOTES ASK YOUR TEACHER The Fish and Game Department stocked a lake with fish in the following proportions: 30% catfish, 15% bass, 40% bluegill, and 15% pike. Five years later it sampled the lake to see if the distribution of fish had changed. It found that the 500 fish in the sample were distributed as follows. Catfish Bass Bluegill Pike 122 83 228 67 LO USE SALT In the 5-year interval, did the distribution of fish change at the 0.05 level? (a) What is the level of significance? State the null and alternate hypotheses. O Ho: The distributions are the same. H, : The distributions are different. O Ho: The distributions are different. H, : The distributions are different. End O Ho: The distributions are different. H,: The distributions are the same. O Ho: The distributions are the same. H, : The distributions are the same. (b) Find the value of the chi-square statistic for the sample. (Round your answer to three decimal places.) Are all the expected frequencies greater than 5? Home Yes O N What sampling distribution will you use? O chi-square O Student's t O uniform normal O binomial What are the degrees of freedom? (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. Since the P-value S a, we reject the null hypothesis. Since the P-value S a, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. At the 5% level of significa on is different than that of five years ago. O At the 5% level of significa is different than that of five years ago