6. You work for a market research firm and have been hired to construct a poll for the company, where they are interested in conducting a survey to find out if customers think they would be willing to buy the product or not. You do not know the probability that a random customer would buy the product, which is why you are conducting the survey. You want to convey to the company the tradeo§ between accuracy (how short the 95% confidence interval will be) and cost (it costs more to increase the sample size). (a) Choosing a sample size of 1000 observations, how wide will the conÖdence interval be if the true probability is one half? (b) How large must the sample size be if we want the confidence interval to be at most 0.01 either side of the sample estimate (use the same probability guess as in (a)?.

You sample 1O0 people to see if they have been to the grocery store in the past week, and find that 85% (.85) of them have been. What is the 95% confidence interval for this study? Leave your answer in decimal format to 2 decimal places. In other words, .04 instead of 3.6% or .11 instead of 11.4%.. O .78 to .92 .84 to .85 O .60 to 1.10 O .60 to 1.00 .15 to 1.55

You are interested in constructing a 90% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 427 randomly selected caterpillars observed, 45 lived to become butterflies. a.  Use 3 decimal places to complete the following statement: With 90% confidence the proportion of all caterpillars that lived to become a butterfly is between  and . b.  If many groups of 427 randomly selected caterpillars were observed, then a different confidence interval would be produced from each group. About  percent of these confidence intervals will contain the true population proportion of caterpillars that become butterflies and about  percent will not contain the true population proportion.

You are interested in constructing a 95% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 390 randomly selected caterpillars observed, 60 lived to become butterflies. Round answers to 4 decimal places where possible. a.  With 95% confidence the proportion of all caterpillars that lived to become a butterfly is between and . b.  If many groups of 390 randomly selected caterpillars were observed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of caterpillars that become butterflies and about percent will not contain the true population proportion.

You create a 95% confidence interval for the proportion of a population. The confidence interval does not contain 0.10. This means that Group of answer choices a.You have evidence to conclude that the population proportion is equal to 0.10. b.You do not have evidence to conclude that the population proportion is equal to 0.10. c.You have evidence to conclude that the population proportion is not equal to 0.10. d.You do not have evidence to conclude that the population proportion is not equal to 0.10. e.The answer cannot be determined with the information given.

You are interested in constructing a 90% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 424 randomly selected caterpillars observed, 50 lived to become butterflies. a.  With 90% confidence the proportion of all caterpillars that lived to become a butterfly is between and . b.  If many groups of 424 randomly selected caterpillars were observed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of caterpillars that become butterflies and about percent will not contain the true population proportion.

I'm having trouble trying to figure out how to work the problem below out.    Let’s say that 44 percent of the 1,300 U.S. adults who responded to a poll about marijuana legalization said they support legalization. Let’s also say the margin of error for the results is +/- 3 percentage points. The margin of error tells us there’s a high probability that nationwide support for marijuana legalization falls: The correct interpretation of this confidence interval is:

Ellie and Alec are each attempting to estimate the proportion of coffee drinkers who consume more than one cup of coffee per day. They each obtain a random sample of coffee drinkers, and, in each sample, the proportion who drink more than one cup of coffee per day is 0.40. Ellie and Alec each use their sample data to construct a confidence interval. Ellie’s interval is from 0.286 to 0.514, and Alec’s interval is from 0.346 to 0.474. One of these intervals was computed correctly, but the other was not. Which interval must be incorrect? A. Ellie’s interval must be incorrect. B. Alec’s interval must be incorrect. C. It’s impossible to answer this question without knowing the level of confidence used for each interval. D. It’s impossible to answer this question without knowing the sample sizes. E. It’s impossible to answer this question without knowing the sample sizes or the level of confidence used for each interval.

2. One of the restaurants participating in Love Week wants to know proportion of Allen residents who plan on coming to their restaurant on their Love Week Spirit Night. If they plan on creating a 96% confidence interval and they want the margin of error to be no more than 3.8%, how large of a sample do they need to get? the lA lo nolh