STATISTICS AND PROBABILITY- ESTIMATION OF PARAMETERS

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\f2. A random sample of 440 voters in a certain district produced 241 voters in favor of candidate M. Estimate the fraction of the population favoring M and place a bound on the error of estimate using 99% confidence interval. Solution STEP 1. n = Confidence level = STEP 2. two conditions that must be met STEP 3. Since a = 0.01 - 1 -0.99 Za/2 = 2.576 STEP 4. p = = 0.55 and q = 0.45 0.55 - (2.576) (0.55)(0.45) (0.55) (0.45) 440 0.55 + (2.576) 140 0.55 - 0.061 0.55 + 0.061 0.489 Class 0.611 48.9% Interval 61.1% a = 0.005 99% 5= 0.005 48.9% 61.1% Conclusion: Therefore, we would estimate the p lies in the interval % to % with confidence coefficient Solve the following problems relating to estimation of parameters. 1. In a graduate teacher college, a survey was conducted to determine the proportion of students who want to major in Mathematics. If 378 out of 900 students said Yes, with 95% confidence, what interpretation can we make regarding the probability that all students in the teacher graduate college want to major in Mathematics. Solution.3. A large appliance store wants to determine the proportion of shoppers at their store that buy a major appliance. They want the estimate to be within 10% of the true proportion and they want to be 90% confident of the results. How large a sample should the store take? Solution