Question

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CHAPTER 11 1. The Fish and Game Department in Wisconsin stocked a new lake with the following distribution of game fish. After five years a random sample of 225 fish from the lake were netted, identified, and released. The Initial Stocking Distribution and Sample Distribution after 6 years are shown in the following table. The Fish and Game Department want to determine if the sample distribution of fish in the lake after six years fits the initial stocking distribution. Use a chi-square hypothesis test to answer their question; us a 5% level of significance. (DO NOT ROUND YOUR CALCULATIONS - USE 4 DECIMAL PLACES) Initial Stocking Distribution FISH OBSERVED: Sample Distribution after 6 years EXPECTED (0-E) (0-EV Pike 10% 40 Trout 15% Perch 20% Bass 25% Bluegill 30% 100% 225 225 (a) State the null and alternate hypotheses and the level of significance (b) Find the critical value(s). Sketch the sampling distribution and show the area corresponding to the critical value. (c) Calculate the sample test statistic from the table above. (d) Based on your answers for parts (a) through (c), will you reject or fail to reject the null hypothesis? Interpret your conclusion in the context of the application.

Answer 1

we have : N= 225 .fish da si = 0.05 level of significance claim :- The fish & Game deportment want to determine of fish in the lake if the sample distribution after six years fits the initial stocking distribution (a) To Test : Ho: The sample distribution of fish in lake after six years not fit the initial stocking distribution rs H,: The sample distribution of fish in the lake after six years fits the initial stocking distribution

Observed Expected Fish 50-E) (0-E12 | I co-E12 sample Initial stocking disht 101: Pince - 40 22-5 Trout 154. 33.75 Perch 201. 38 45 -7 17:5 306.25 13.6111 -13.75 189.0625 5.6018 49 L 1.0988 5-75 L 33.0625 0.5877 ] -2.5 6.25 0.0925 20.9819 Bass 25". 62 56.25 Bluegill 3095. 65 67.5 E= I 100%. 225 l 225

© critical value = Na de here df = ckall here k=5 = of=La Xbos, 4 = 19.488 ]-chom chi-square fable) © Test statistics = x= { 10;-&;)? = 120.9819| Ei

we reject Hol, because g2 rest statshic > x2 critical value Conclusion in there is sufficient evidence to conclude that the sample distribution of fish in the lake after six years fits the initial distribution at a= 0.05 level stocking of significance.
we reject Ho hence result is significant