Question

For the following data:

1 2 3 4 3 6 6.6 7.1 7.8 4.7 8.5 5.4

a. Calculate the sample mean and sample variance

b. Calculate the probability that the population mean is between 9 and 10 if the population standard deviation is known to be 1.5.

c. What is the 98% confidence interval for the population mean if the population standard deviation is known to be 1.5?

d. Calculate the 98% confidence interval using the sample standard deviation.

Answer 1

DATE: a> sample mean ža Exi ( 4001 6 sample mean. 6-68" sample variance 1 Exie x2 1 (2783) (6.683) ² B-1 sample yansances 1o.gggs is by Prolo. that the populaboo mean berdeen g and the pojould Sanelarrel deujaton. chacon to 사 fire. p[ glaceo] =pg-x Luc lonx 10-6.68 IS d19-6-68 15 E $(2-2113) – $(1.5446) 0.986 0-939 pige u<ro 0.047 CS Scanned with CamScanner

PAGE NO.: DATE: - - с. 98 y. C- I for the popela mean it Standard deusation is os 1.5 (formula: ět zx * 5 2 Here 002 ED L= 0:01 P Z = 2-326 G.683 + 2326 1.5 vo 6:683 + 1.42438 8.10738 Upper limita Lower limit 9.2586 987 C-T meas is for the populo S-2586 18.1074 calcolate Standard 98%o. I using sample deviation. | Gample Standard deviations = sample mariance 10.9995 - 3.3165 CS Scanned with CamScanner

PAGE NO.: DATE: - Here, X=002 =p 0 2 ten, oool) = tis,001) 3.365. formulae. ł - tentoof)* S / 6.683 + 3.365 * 3.3165 6.683 + 4.556 Upper Limit = lower limit 114239 2-1268 98% confidence interval for the population mens H239 (1 2-1268 [11.239]). Cs Scanned with CamScanner