Question

Question 9 An experimenter flips a coin 100 times and gets 58 heads. Test the claim that the coin is fair against the two-sided claim that it is not fair at the level a=.01. a) O H.:p= .5, Ha:p> .5; = = 1.62; Fail to reject H, at the 1% significance level. b) O Ho: p= .5, Ha:p #.5; == 1.60; Fail to reject H, at the 1% significance level. c) O H.:p= .5, H.:P > .5; == 1.60; Reject H, at the 1% significance level. d) O H.; p= .5, Ha:p #.5; == 1.62; Fail to reject H, at the 1% significance level. e) O H.:p=.5, HipH.5; = = 1.60; Reject H, at the 1% significance level. Review later

Answer 1

Solution: Sample size = n = 100 Sample number of heads = x = 58 Sample proportion of heads: x 58 p = -= = 0.58 n 100 Null Hypothesis: Ho:p = 0.5 Alternative Hypothesis: H :p # 0.5 Standard error of the estimate: p(1 - p) 0.5 x (1 – 0.5) -= 0.05 V n ✓ 100 Test Statistic: Ô - p Zstat = Op 0.58 – 0.5 → Zstat = - -= 1.60 0.05 P-value: From normal distribution table; the area in the upper tail to the right of (z = 1.60), is given by: 0.0548 The test is a two-tailed test. Hence, p-value = 0.0548 x 2 = 0.1096 Level of significance =a=0.01 Since p-value > a, we fail to reject the null hypothesis Ho. Hence, Option-B is the correct answer