Question

2. For the following data: 1 2 3 4 5 5 6 16 20 18 17 18 21 1. 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 2.3. c. What is the 95% confidence interval for the population mean if the population standard deviation is known to be 2.32 d. Calculate the 95% confidence interval using the sample standard deviation.

Answer 1

Page-1 Answer: As per given details 2.0) The Sample ī Exi mean is 131 = 10.92 12 The Sample variance is S": {(29-3)”. E (19-10.92) - 63.174 n-1 12-1 b) The Poobabalady that the population mean % between q and 10 S. P (QCMCO) P(-10C-4 (-9) =P (10.92 -10 <-<10.92-9) 10.92-10 PL 10.92-9 2.3/112 P(1.386<2 <2.892) = P12<2.892) - P(2<1:386) = 0.9981 -0.9171 = 0.081 c) the 95% confidence interval for the prolation C M-u Elin 2:31512 mean is.

Page-2 = a + 1.96 * 2.3 via - 10.92¢1.96 * 2.3 12 = 10.92€ 1.301 9.619, 12.221 d) The 95% confidence interval using the sample standard deviation is given by. ñ I talan-1* si Here, the degree of freedom os = 12-1=11 The critical t-value is 2.201 So, the 95% confidence anterval és 10.92 +2.2014 7.948 12. = 10.92 + 5.05 = 5.87, 15.97 PLEASE HIT LIKE VOTE