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- In exploring possible sites for a convenience store in a large neighbourhood, the retail chain wants to know the proportion of ratepayers in favour of the proposal. If the estimate is required to be within 0.1 of the true proportion, would a random sample of size n = 100 from the council records be sufficient for a 95% confidence interval of this precision?3.Michael wants to make a confidence interval estimate for the proportion of community members in favor of a tax increase for more local school funding. If he wants the margin of error to be no more than 0.025 at a 90% confidence level, a)What is the required sample size required to obtain the desired margin of errorin a study of government financial aid for college students, it becomes necessary to estimate the percentage of full-timecollege students who earn a bachelor's degree in four years or less. Find the sample size needed to estimate that percentage. Use a 0.02 margin of error and use a confidence level of 90%. a. Assume that nothing is known about the percentage to be estimated. (Round up to the nearest integer.)
- Suppose that the sample size had been 240, with x bar=4.1 and s=3.1. Use technology to find a 95% confidence interval. Describe the effect of sample size on the margin of error.2. The National Health Statistics Reports dated Oct. 22, 2008, included the following information on the heights (in.) for non-Hispanic white females: Age Sample Size Sample Mean Std. Error Mean 20-39 866 64.9 .09 60 and older 934 63.1 .11 a. Calculate and interpret a confidence interval at confidence level approximately 95% for the difference between population mean height for the younger women and that for the older women. (answer I found is (1.5214 , 2.0786)) b. Let denote the population mean height for those aged 20-39 and denote the population mean height for those aged 60 and older. Interpret the hypotheses and , and then carry out a test of these hypotheses at significance level .001 using the rejection region approach. (answer I found is = Reject the null hypothesis (p-value is less than the level of significance) c. What is the P-value for the test you carried out in (b)? Based on this P-value, would you reject the null hypothesis at any…After Texas A&M lost again to their rival, the University of Texas, in a football game, the A&M Alumni association decided to conduct a survey to see who wanted to fire the head football coach. Let p represent the proportion of all alumni who favor firing the coach. To guarantee an estimate that is within 0.05 of p at the 95% confidence level, which of the following is the smallest sample size needed? a 269 b 1436 c 385 d 601 e 421
- 2. Compute the margin of error of p given the following: Confidence level 97%, p 0.85, n 120. 3. Compute the confidence interval estimate given the following: Confidence level 99 %, p= 0.4, n 40. 4. In a survey participated by 100 college students, it was found that 60% of them have personal computers at home. Construct a 95% confidence interval estimate of the true proportion of all college students who have personal computers at home. 5. A politician engaged the services of a private opinion pollster to determine the sample size needed among his constituents to interview about their perceptions on the freedom of information bill. Previous polls revealed that approximately 62.5% are in favor of the bill. The politicians adopted the 95% level of confidence within an error of 2%. How large a sample does the pollster need?A soft-drink manufacturer purchases aluminum cans from an outside vendor. A random sample of 70 cans is selected from a large shipment, and each is tested for strength by applying an increasing load to the side of the can until it punctures. Of the 70 cans, 59 meet the specification for puncture resistance. (a) Find a 95% confidence interval for the proportion of cans in the shipment that meet the specification. (b) How to interpret the confidence interval in part (a)? (c) Find the sample size needed for a 90% confidence interval to specify the proportion to within ±0.06. (d) If a 90% confidence interval is computed each day for 300 days, what is the probability that more than 280 of the confidence intervals cover the true proportions?4.) A simple random sample of size n is drawn from a population that is normally distributed. Using the data, it was found to be: x-bar = 108, and s = 10. Construct a 95% confidence interval about μ if the sample size is 25. Construct a 95% confidence interval about μ if the sample size is 10. Compare your results from Parts (a) and (b). How does decreasing the sample size affect the margin of error? Construct a 90% confidence interval about μ if the sample size is 25.
- From a simple random sample of 400 of the 1,395 colleges in our population, it was found that business statistics was a two-semester course in 141 of the sampled colleges. Estimate the proportion of all colleges for which the course is two semesters long, and find a 90% confidence interval.In a previous study, it was found that p hat=.73 for a particular sample. Suppose we would like to repeat this study. Give the sample size n, required to have the margin of error equal to .01, at the 98% confidence level.A national opinion poll found that 44% of all American adults agree that parents should be given vouchers that can be applied toward their children's education at any public or private school of their choice. The result was based on a small sample. A)How large an SRS is required to obtain a margin of error of at most 0.03 in a 99% confidence interval? B) Answer the question in part A again but this time By using Phat=0.5. By how much do the two sample size differ?