Question

How much does a sleeping bag cost? Let's say you want a sleeping bag that should keep you warm in temperatures from 20°F to 45°F. A random sample of prices ($) for sleeping bags in this temperature range is given below. Assume that the population of x values has an approximately normal distribution.

80 65 95 90 105 100 30 23 100 110 105 95 105 60 110 120 95 90 60 70

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean price x and sample standard deviation s. (Round your answers to two decimal places.)

x = $

s = $

(b) Using the given data as representative of the population of prices of all summer sleeping bags, find a 90% confidence interval for the mean price μ of all summer sleeping bags. (Round your answers to two decimal places.)

lower limit $

upper limit $

Answer 1

Solution: Given that 80,65,95,90,105,100,30,23,100,110,105,95,105,60,110,120,95,90,60,70

sample n = 20, 90% Confidence interval

df = n-1 = 19, t = 1.729

(a) x = 85.40
  
s = 26.40 (rounded)

(b) 90% Confidence interval for the mean price μ = X +/- t*s/sqrt(n)
= 85.40 +/- 1.729*26.40/sqrt(20)
= (75.1933 , 95.6066)
= (75.19 , 95.61) rounded

lower limit = 75.19$
upper limit = 95.61$
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X = sum of term /number of terms = 1708/20 = 85.4

standard deviation :