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- You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately ˆp=90%p^=90%. You would like to be 99.5% confident that your esimate is within 1.5% of the true population proportion. How large of a sample size is required? I must have tried this question and ones similiar to it a dozen times. Can you break this down for me so I understand I'm doing wrong? Thank you!arrow_forwardYou want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately ˆp=22%p^=22%. You would like to be 99% confident that your esimate is within 1.5% of the true population proportion. How large of a sample size is required?arrow_forwardYou may need to use the appropriate appendix table or technology to answer this question. The following results are for independent random samples taken from two populations. Sample 1 Sample 2 n1 = 20 n, = 30 X1 = 22.7 X2 = 20.1 s, = 2.3 2 = 4.6 (a) What is the point estimate of the difference between the two population means? (Use x, - x,.) 2.72 (b) What is the degrees of freedom for the t distribution? (Round your answer down to the nearest integer.) 48 (c) At 95% confidence, what is the margin of error? (Round your answer to one decimal place.) 1.9 (d) What is the 95% confidence interval for the difference between the two population means? (Use x, - Round your answers to one decimal place.) .6 to 4.4arrow_forward
- The amounts of a chemical compound y that dissolved in 100 grams of water at various temperatures x were recorded. The data were coded and recorded in the accompanying table. Use this information to answer parts a through c. a) Evaluate s^2. s^2 = _____ (Round to two decimal places as needed.) b) Construct a 99% confidence interval for beta 0 _______ < beta 0 < _______(Round to three decimal places as needed.) c) Construct a 99% confidence interval for beta 1 ________ < beta 1 < _________ (Round to three decimal places as needed.)arrow_forwardOn minitab or excel Calculating the coefficient of determination of a set of data, it was obtained that r^2 = 0.845 . Based on this value, it can be concluded that: Options: The least squares line provided a good fit as a large proportion of the variability in "y" has been explained by the least squares line. The least squares line provided a good fit as a small proportion of the variability in "y" has been explained by the least squares line. The least squares line did not provide a good fit since a small proportion of the variability in "y" has been explained by the least squares line. The least squares line did not provide a good fit since a large proportion of the variability in "y" has been explained by the least squares line.arrow_forwardHow do you solve these problems?arrow_forward
- The melting points of two alloys used in formulating solder were investigated by melting 21 samples of each material. The sample mean and standard deviation for alloy 1 was īi = 420°F and si = T2 = 426°F and s2 = 3°F. Find a 95% confidence interval on the difference in 4°F , and for alloy 2, they were %3D the two means. (-0.061, 0.861) -4.119, 15.129) (-8.205, –3.795) (1.857, 18.943)arrow_forwardPlastic sheets produced by a machine are periodically monitored for possible fluctuations in thickness. Typically, a variance in thickness around 1.95 square millimeters is regarded as acceptable. As part of quality control, a random sample of 30 plastic sheets are taken and the sample variance is calculated to be 3.17. Assume that the population is normally distributed. Let a = 0.05. - (a) Construct a confidence interval for population variance at (1 − a) confidence level. (b) Test against an upper-tail hypothesis that the true population variance is larger than 1.95.arrow_forwardHistograms of random sample data are often used as an indication of the shape of the underlying population distribution. The histograms on below are based on random samples of size 30, 50, and 100 from the same population. (a). Complete the table giving the range of the sample data in each of the histograms. (refer to picture of table) (b). Based on the completed table, select the most reasonable estimate of the range of the population data. A. 10 to 15 B. 9 to 14 C. 9 to 15 D. 11 to 13arrow_forward
- ANOVA is based on an F-ratio that is calculated as the ratio of two variance estimates, the variance between groups and the variance within groups, but enables conclusions to be made about the means of the samples involved. What is the logic of that? I.e., explain the rationale that supports the use of variance estimatesarrow_forwardX1=60 N1=37 S1=12 X2=50 N2=39 S2=6 Confidence interval 80% Find the point estimate.arrow_forwardFor each residual plot below, decide on whether the usual assumptions:"Yi=B0+B1xi+ei,i=1,…,n,e1 independent N(0,sigma^2) random variables" of simple linear regression are valid or not.If some assumptions seem invalid, choose the options(s) which indicate the most obvious departures from the model assumptions. Note : For a small sample, the normality assumption cannot be "proved", but it can be "violated" if there is an extreme residual (outlier).Part a) y-axis has residual, x-axis has x-variable with values 1,2,...,10. (Click on graph to enlarge) Which is/are the best answer(s) for the residual plot (a)?A. linear relation assumption is invalidB. constant variance assumption is invalidC. assumptions seem reasonableD. the normality assumption is invalidE. None of the abovePart b) y-axis has residual, x-axis has x-variable with values 1,2,...,10. (Click on graph to enlarge) Which is/are the best answer(s) for the residual plot (b)?A. constant variance assumption is invalidB. the…arrow_forward
- Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt