Question

1. Find the sample size needed to estimate the proportion of houses that have security systems if the sample proportion h = 0.19, the margin of error is 0.02, and the confidence level is 90%. 2. Suppose that in a random sample of 50 adults, 41 were registered to vote. Construct a 95% confidence level interval for the population proportion of registered voters.

Answer 1

Here given P = 0.19 E 0.02 - consider C1-0) 100.1. = 901 1 - W=0.90 x=0:1 by using standard normal table 242 1.645 NOW, Sample size - Zain . Ñ CI-ê) E2 = C1.645)x0:19 C1-0:19) (0.02)2 7041:14 3 1042 sample size needed to estimate the proportion of houses that have security system is 1042 Ans: 1042

2) Here, in a dandom sample of 50 adults 41 were registered to vote <a 41 SO n = 50 consider, (1-2) 100.4. = 951 1-0 =0.95 d=0:05 by using standaod normal table ZX12 = 1.96 Wow, confidence interval - Cô - Zapyt [C-6) P = FC 0.82 -1.90X 0.82C1-0-82), SO 0.82 + 1.96 X 0.82 (1-0.82) so 2)) 0.714 10.926 Therefore, 95.4. confidence interval for the popuation proportion of registered (0.714.) 0.926) voters is