Question

A paint manufacturer uses a machine toll gallon cars with paint (1 128 ounces). The manufacturer wants to estimate the mean volume of paint the machine is puting in the card within 0.5 ounce Assume the population of volumes is normally distribuid. (8) Determine the minimum sample size required to constructa 90% confidence interval for the population mean. Assume the population standard deviation is 0.71 ounce (0) The sample meanis 126.75 ounces with a sample size of 9, a 90% level of confidence and a population standard deviation of 0.71 ounce does it sem possible that the population mean could be exactly 128 ounces? Explain Click here to view page 1 of the Standard NormalTable Cick here to view page 2 of the Standard NormalTable cans (a) The minimum sample size required to construct a 90% confidence intervalis (Round up to the nearest whole number.) sem possible that the population mean could be exactly 128 ounces because 128 ounces fails the confidence interval (b) The 90% confidence interval for a sample size of 9 is (Round to two decimal places as needed)

Answer 1

Given; E0.5 0.0.71 2 * = 1.645 (Atx 0.10 0.05, from a- table) ca) To find minimum sample size required Dezt Dez* 62 1.645 X 0.71 2 0.5 n = 2.3359)2 n = 5.456 Inñol (b) X = 126.75:no9; 5.0.71 The got confidence interval is 7 ± 2* olun (Z*1-645, 0.05 (from za table 126.75 1645 x 126.75 + 0.3893 The go % confidence interval is (126.36 127.14)

the 90% confidence interval for sample size 9 is ( 126.36 , 127.14 ). It does seems possible that the population mean could be exactly 128 ounces because 128 ounces falls outside the confidence interval.