Question

2. For the following data: 2 3 4 5 6 12 10 9 8 5 13 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 3. c. What is the 90% confidence interval for the population mean if the population standard deviation is known to be 3? d. Calculate the 90% confidence interval using the sample standard deviation.

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Rawan Badran

Answer 1

PAGE NO.: DATE: - from the given simple data set ay sample mean = x= 1 Exi ( 57 ) 6 Soonple Mecima Х 9.5 sample variance S2 s² = exi²_.x2 n-l (583.)-(9.5) 2 5 sample Kanianses,32 =126.35 sample Standard deisation - s2 ta 26.35 5 5.133 61 15 be 3. O=3 Prob. that that the popu? between g and if the populo Gendard deviation is knowo to ine Here, sample is unbiased estimator of the popul? megn W = 9.5 mean = ا cs Scanned with CamScanner

PAGE NO. : DATE: - poob. od g to Hence, Here we calcalate that sample meas lise between lo. when JE 3. Lire plgc c* <10]=P[ g-al <ř< lots ohm ohn < 2 pl 9-9.5 3/G se- orn 10-9:5 3 WG EP -0.4062 (Z < 0.4082 p[-Zx Lec i za $(26) - -2x) 4 (0:4082)- $ (-0.4082) 0.658~0.342 p[gci <10] = 0.316 for goy ey Formula jf cil for populn is mean 3 za 0 rñ cs Scanned with CamScanner

PAGE NO.: DATE: Here Q=0.10 x -0.05 Z 10.os) = 1.645 3 9.5 I 1.645 * vñ gost 2-0147 upper limit= 11:5147 Lower limit E7-48 $3. go y C. I for the popull mean is if = 3 7.4853 11:5147 90 C. meçs it dy Formula for popu? deusation $ = 5.133 for the Sample Standard calcalated above i5 در کر ری že tinol, a) * * To Here Q=0.10 I f = 0.05 tcnt,&/2) = ti (5,0.05) 2.0lso cs Scanned with CamScanner

PAGE NO.: DATE: - 9.5 I (2.0150 * 54133 VG gis I 4.2225 PD Npper limit: 13.-12 25 lower limit = 5.2775 90 y CI mean ured deviation is for population simple standardod S-133 5.2775 13.7225 cs Scanned with CamScanner