Question

The business college computing center wants to determine the proportion of business students who have personal computers (PC's) at home. If the proportion exceeds 30%, then the lab will scale back a proposed enlargement of its facilities. Suppose 250 business students were randomly sampled and 75 have PC's at home. Find the rejection region for this test using a -0.05. Reject Hifz > 1.645. Reject Holf z > 1.96 or z < -1.96. Reject Hifz - 1.645. Reject HO If z < -1.645,

Answer 1

Let p denotes the population proportion. Hypotheses : To test null hypothesis Ho :p=0.3 against alternative hypothesis Hi : p > 0.3 Let o denotes the sample proportion and n denotes the sample size. Here, os 75 250 0.3000, n = 250, standard error 0.3 * (1 – 0.3) 250 = 0.028983 The test statistic can be written as: 2= (p - po) Po*(1-P) n which under H, follows a standard normal distribution. Decision rule / Rejection region : We reject Ho at 0.05 level of significance if P-value < 0.05 or if ZSTAT > 20.05 = 1.644854 0.4 0.3- density 0.2- 0.1 - 0.0- U- -4 -2 NO-

Reject H₀ if z > 1.645