763 An urn contains marbles that are either red or blue To t

7.63. An urn contains marbles that are either red or blue. To test the hypothesis of equal proportions of these colors,
we agree to sample 64 marbles with replacement, noting the colors drawn and adopt the following decision rule:
(1) accept the hypothesis if between 28 and 36 red marbles are drawn; (2) reject the hypothesis otherwise. (a)
Find the probability of rejecting the hypothesis when it is actually correct. (b) Interpret graphically the decision
rule and the result obtained in (a)

Solution

a.)The Probabilityof not getting between 28 and 36 red marbles are drawn.If th color is fair equals to 1-0.9642=0.0358

the probability of rejecting the hypothesis when it is actually correct=0.0358.

B.)The desicion of the rulewhich the probability of marbles that are either red or blue.ifwe agree to sample 64 marbles with replacement score is between -2.10 to 2.10.

we accept the null hypothesis otherwise we reject the null hypothesis marble is not fair.

The error made be reject the null hypothesis when it should be accepted is the Type I error of the decision rule and the probability of making error is equals to 0.0358 from part a