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Paul Tucker HW 6 STAT 280 Thomas 7.05 a. b. 7.06 a. b. xbar = 2.1429 the sample point most likeley falls within .64 of the population mean xbar = margin of error (20,200, 69,800) $45,000 $24,800 c. from to a point estimate does not indicate precision (how likely we are close to actuality). A confidence interval does. Also, it seems like the mean cou between 20,200 and 69,800, this is a wide area outside of 45,000. 7.12 a. n = 987 x = 17 phat = 17/987 se = [phat(1phat)/n] margin of error = z(se) phatz(se) 987 0.02 0 0.01 b. c. d. .0172241.96(.004141) 0.03 (.0091, .0253) 0.01 With 95% confidence, it seems as though between 0.91% and 2.5% of x = 1764 n = 2565 phat = .6877 95% CI = (.670, .706) "sample p" = x/n 1764/2565 7.15 a. b. c. with 95% confidence the GSS reports that between 67% and 70.6% of death penalty for people convicted of murder. 95% confidence in the long run means that over many evaluations of su method will estimate an interval that contains the real parameter correc d. because our lowest value is over .50, then we may conclude over half f 1.65 2.32 3.27 497 3.02 2 1.81 0.08 7.18 z score for 90% confidence z score for 98% confidence z score for 99.9% confidence 7.25 a. n= xbar = q2 = s= se = s/((n)) b. c. d. 7.27 a. b. c. we have 95% confidence that the population mean falls between 2.89 a no, because 2 falls outside our confidence interval df = 4, CI = 95% t* = 2.776 df = 14, DI = 95% t* = 2.145 df = 14, CI = 99% t* = 2.997 margin of error = 1.96(se) se = s/((n)) 5 2.5 7.37 s = 100 n = 400 n = 1600 CI = 95% larger n, smaller margin of error (and therefore tighter confidence interval) 7.38 s = 100 n = 400 CI = 95% CI = 99% se = s/((n)) margin of error = 1.96(se) margin of error = 2.576(se) 5 larger % CI, larger margin of error (and therefore, wider interval) 7.43 n = (phat(1phat)z^2)/(m^2) phat = 0.44 1phat = 0.56 z = 1.96 z^2 = 3.84 m = .05 m^2 = 0 n= 378.63 need at least 379 people 7.46 n = (phat(1phat)z^2)/(m^2) phat = 0.48 1phat = 0.52 z = 1.96 z^2 = 3.84 m = .025 m^2 = 0 n= 1534.18 need at least 1535 people 7.48 if we guess that xbar 3s covers almost all the population, and that range is from 120,000), then 6s covers the range of 120,000. letting 120,000 = 6s, we can approximate s as equal to 20,000. using a tscore of 2.7 (~df>30), we may set up problem as thus: n = (2.7^2)(20,000^2)/(1000^2) t* = 2.7 2916 s = 20,000 m = 1,000 We need approximately 2,916 participants. 7.70 a. b. margin of error is dependent upon sample size (see 7.37). In general, a sample size increases, margin of error decreases this gives us xbar, but not the sample error, which depends on a standa deviation. We don't have enough to calculate the sample error. n (sample size) df 10 20 30 infinity infinity 7.71 a. 9 19 29 b. as df approaches infinity (ie, as sample size increases), the t distributio approaches a standard normal distribution. n = (phat(1phat)z^2)/(m^2) phat = 0.5 1phat = 0.5 z^2 = 3.84 m^2 = 0 7.88 z = 1.96 m = .05 n= 384.16 need at least 385 people ithin .64 of the population mean 95% confidence interval $20,200 $69,800 recision (how likely we are close to the parameter in es. Also, it seems like the mean could actually fall anywhere a wide area outside of 45,000. 0.98 0.02 241.96(.004141) hough between 0.91% and 2.5% of all adults in the US were victims. ple p" = x/n 0.69 ts that between 67% and 70.6% of all respondents favor the of murder. ans that over many evaluations of survey data using this contains the real parameter correctly 95% of the time. 0, then we may conclude over half favor the penalty opulation mean falls between 2.89 and 3.21 dence interval Margin of Error 1.96(5) 1.96(2.5) 9.8 4.9 ore tighter confidence interval) 1.96(5) 2.576(5) Margin of Error 9.8 12.88 efore, wider interval) e population, and that range is from (0, letting 120,000 = 6s, we can ore of 2.7 (~df>30), we may set up the 2.7 20000 1000 ample size (see 7.37). In general, as ror decreases le error, which depends on a standard o calculate the sample error. tscore = .025 2.26 2.09 2.05 1.960 mple size increases), the t distribution ibution. ...
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 Spring '08
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