How much does a sleeping bag cost Lets say you want a sleepi

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.

(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.)

(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 of all summer sleeping bags. (Round your answers to two decimal places.)

Solution

a)
Mean(x)=83.4 ~ 84
Standard deviation( sd )=28.37 ~ 29

Confidence Interval
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval

Sample Size(n)=20
Confidence Interval = [ 84 ± t a/2 ( 29/ Sqrt ( 20) ) ]
= [ 84 - 1.729 * (6.485) , 84 + 1.729 * (6.485) ]
= [ 72.788,95.212 ] ~ [ 73,96]