The NWBC found that 16.5% of women-owned businesses did not pro- vide any employee ben- efits. What sample size could be 99% confident that the estimated
... [Show More] (sam- ple) proportion is within 6 percentage points of the true population propor- tion? Question Suppose a market re- searcher wants to deter- mine the current percent- age of online shoppers who are males. How many online shoppers should the researcher survey in order to be 90% confident that the estimated (sam- ple) proportion is within 3 percentage points of the Correct an- swers:$254$254 EBP = 6%. ±=0.01T. he z-score is found 0.012=0.005=z±2=2.576 n=(z±2)2p(Ù2)(q2)EBP2 =(2.5762)(0.165)(0.835)0.06 n=253.96 Rounded up to 254 peo- ple. Correct an- swers:$752$752 Given the information in the question, EBP=0.03 since 3%=0.03 and z±2=- z0.05=1.645 because the confidence level is 90%. The values of p2 and q2 are unknown, but using a value of 0.5 for p2 will result in the largest pos- sible product of p2q2, and thus the largest possible n. Question A recent survey asked 1,379 top executives about business trends. The surveyed showed that 23% want to strengthen in- novation to capitalize on new opportunities. What is the value of q2 as a deci- mal? Round to the nearest hundredth. Answer Explanation Correct answers: 0.77 The value of q2 is: 1 p2=1 0.23=0.77 Correct an- swers:1$0.652$0.652 2$0. To form the sample pro- portion, take the number Question Alice wants to estimate the percentage of people who own a mountain bike. She surveys 230 individu- als and finds that 150 own a mountain bike. What are the sample proportions for of successes, and divide it by n, the number of tri- als. In this scenario, the number of successes is the number of people who own a mountain bike, 150. The total number of peo- ple surveyed was 230. p2=xn=150230=0.652 successes, p2, and failures,So, p2=0.652 is the sample q2? Round your answers to three decimal places. proportion, which is the point estimate of the pop- ulation proportion. Since p2+q2=1, we can solve for q2.q2=1 p2=1 0.652=0.3 Correct Using p2=0.652, q2=0.348,an- and n=230, what is the 95% confidence interval for the proportion of the population who own a mountain bike? swers:1$0.590$0.590 2$0. We know n=230, p2=0.652, and q2=0.348. Since the confidence level is 95%, ±=1 0.95=0.0a5n,d ±2=0.025T. he z-value for Use the table of common z-scores above. Round z0.025 is 1.96. EBP=(z±2)(- p2q2n )=(1.96)((0 your answers to three dec- imal places. The Parameters for a Con- fidence Interval with a Pro- portion So we can write the confidence interval as (0.652 0.062,0.652+0.062) The procedure to find the confidence interval for a proportion is similar to that for the population mean, but the formulas are a bit different. We are still look- ing for a range of numbers, written as: (point estimate - margin of error, point es- timate + margin of error), with (point estimate - mar- gin of error) as the lower value and (point estimate + margin of error) as the upper value of the confi- dence interval. Since we're looking for a point estimate for the true proportion and mar- gin of error for proportions here, instead of means, the point estimate will be the sample proportion, p2, Finding the Sample Pro- portion (p2) and the margin of error will be the error bound for the proportion (EBP). How do you know you are dealing with a proportion problem? First, the under- lying distribution is a bino- mial distribution, and there is no mention of a mean or average. If X is the bino- mial random variable, then X [Show Less]