Question 4 (1 point) Listen ? Saved A researcher wants to construct a 90% confidence interval for the proportion of elementary school students in the local county who ride the bus home on a regular basis. What sample size is needed so that the confidence interval will have a margin of error of 6%.
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The formula for calculating the sample size needed for a proportion with a specified margin of error is: n = (Z^2 * p * (1-p)) / E^2 where: n = sample size Z = Z-score corresponding to the desired confidence level (for a 90% confidence level, Z = 1.645) p = Show more…
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1) A sample of size n is drawn from a population whose standard deviation is σ. Find the margin of error for a confidence interval for μ. 2) A researcher wants to construct a 98% confidence interval for the proportion of elementary school students in Seward County who receive free or reduced-price school lunches. What sample size is needed so that the confidence interval will have a margin of error of 0.09? 3) An Internet service provider sampled 540 customers and found that 55 of them experienced an interruption in their service during the previous month. Construct a 95% confidence interval for the proportion of all customers who have experienced a service interruption. 4) Use the given data to construct a confidence interval of the requested level. x = 78, n = 124, confidence level 98%
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Q4. Suppose a cell phone manufacturer would like to know what proportion of its customers are dissatisfied with the service received from their local distributor. The customer relations department will survey a random sample of customers and compute a 97% confidence interval for the proportion that are dissatisfied. From past studies, the department believes that this proportion will be about 0.10. a. Find the sample size needed if the width of the confidence interval is to be no more than 0.06. b. Find the sample size needed if the width of the confidence interval is to be no more than 0.06 and no information from past studies is provided.
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