Question

Learning to ski as an adult can be a daunting task. Many ski resorts offer skiing lessons for adults with the hope of increasing attendance. Ski University would like to advertize their quality ski instructors by estimating the population mean number of lesson hours it takes for adult learn-to-ski participants to "graduate" from their program, that is, to ski comfortably on their own. A random sample of 27 recent adult learn-to-ski participants at Ski University was obtained, and each was asked to report the amount of lesson hours they took to graduate. As a result of the study, a 98% confidence interval was found to go from 2.4 lesson hours to 4.6 lesson hours.

1. Estimate of the population mean number of lesson hours it takes to graduate for all recent adult learn-to-ski participants at Ski University.

2. Choose the correct answer: We estimate, the average distance of the possible _______________ (for repeated samples of the same size n) from the ___________ to be about ______ lesson hours.

a. population mean value μ, sample mean values (x̄ values), 0.4437

b. sample mean values (x̄ values), population mean value μ, 0.4437

c. population mean value μ, sample mean values (x̄ values), 0.4448

d. sample mean values (x̄ values), population mean value μ, 0.4448

e. population mean value μ, sample mean values (x̄ values), 2.3055

f. sample mean values (x̄ values), population mean value μ, 2.3055

g. population mean value μ, sample mean values (x̄ values), 2.3112

h. sample mean values (x̄ values), population mean value μ, 2.3112

3. Choose the correct answer: We estimate, the average distance of the possible _______________ from the ___________ to be about ______ lesson hours.

a. sample mean value , sample values, 0.4437

b. sample values, sample mean value , 0.4437

c. sample mean value , sample values, 0.4448

d. sample values, sample mean value , 0.4448

e. sample mean value , sample values, 2.3055

f. sample values, sample mean value , 2.3055

g. sample mean value , sample values, 2.3112

h.sample values, sample mean value , 2.3112

Answer 1

Ques. No. 1 This is a symmteric CI, hence sample mean (which is point estimate of the population mean) is x = (2.4 + 4.6)/2 = 3.5 Best estimate of population mena-x - 3.5 Margin of error = x Length of C-(24-4 6) /2 = 1.1 E = 1.1 CI is 3.5 ± 1.1 2 The Critical Value -ta/2 to.o 2.479 E-t * s/vn s--ryn-_ * V27 ~ 2.3056758 2.306 1.1 2.479 We estimate, the average distance of the possible sample mean (for repeated samples of the same size n) from the population means to be about 2.3055 lesson hours. 3) Same as (2)