Question

8.3.17 Construct an 80% confidence interval to estimate the population mean using the data below. X = 19 S = 4.6 n=23 What assumptions need to be made about this population? The 80% confidence interval for the population mean is from a lower limit of to an upper limit of (Round to two decimal places as needed.)

Answer 1

Lower limit = 17.73

Let T denotes the sample mean, s denotes the sample standard deviation and n denotes the sample size. Here, 4.600 T = 19.000, sº = 21.160000, 8 = 4.600, n = 23, standard error 0.959166 ~ 0.959 V23 = The critical value is tcritical = t 1-0,3,22 to.1,22 1.321237 1.321 At 80 percent confidence level, The margin of error is: S 4.600 4.600 ME= * to.1,22 *t 1-0.8 ,22 2 *1.321 = 1.265000 1.2650 vn V23 V23 a 80 percent confidence interval of population mean u is S =ī + *t 1-0.8 ,22 п 2 4.600 = 19.000 + * 10.1,22 V23 4.600 = 19.000 € * 1.321 23 = 19.000 + 1.265 = (17.735000, 20.265000) = (17.73,20.27)

Upper limit = 20.27