In a fishing lodge brochure, the lodge advertises that 75% ofits guests catch northern pike over 20 pounds. Suppose that lastsummer 65 out of a random sample of 88 guests did, in fact, catchnorthern pike weighing over 20 pounds. Does this indicate that thepopulation proportion of guests who catch pike over 20 pounds isdifferent from 75% (either higher or lower)? Use ? = 0.05. (a) Whatis the level of significance? State the null and alternatehypotheses. H0: p = 0.75; H1: p ? 0.75 H0: p < 0.75; H1: p =0.75 H0: p = 0.75; H1: p > 0.75 H0: p ? 0.75; H1: p = 0.75 H0: p= 0.75; H1: p < 0.75 (b) What sampling distribution will youuse? The Student's t, since np > 5 and nq > 5. The Student'st, since np < 5 and nq < 5. The standard normal, since np< 5 and nq < 5. The standard normal, since np > 5 and nq> 5. What is the value of the sample test statistic? (Round youranswer to two decimal places.) (c) Find the P-value of the teststatistic. (Round your answer to four decimal places.) Sketch thesampling distribution and show the area corresponding to theP-value. WebAssign Plot WebAssign Plot WebAssign Plot WebAssignPlot (d) Based on your answers in parts (a) to (c), will you rejector fail to reject the null hypothesis? Are the data statisticallysignificant at level ?? At the ? = 0.05 level, we reject the nullhypothesis and conclude the data are statistically significant. Atthe ? = 0.05 level, we reject the null hypothesis and conclude thedata are not statistically significant. At the ? = 0.05 level, wefail to reject the null hypothesis and conclude the data arestatistically significant. At the ? = 0.05 level, we fail to rejectthe null hypothesis and conclude the data are not statisticallysignificant. (e) Interpret your conclusion in the context of theapplication. There is sufficient evidence at the 0.05 level toconclude that the true proportion of guests who catch pike over 20pounds differs from 75%. There is insufficient evidence at the 0.05level to conclude that the true proportion of guests who catch pikeover 20 pounds differs from 75%.
