//How much does a sleeping bag cost? Let\'s say you want a sleeping bag that sho
ID: 3269211 • Letter: #
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.
(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 of all summer sleeping bags. (Round your answers to two decimal places.)
lower limit $
upper limit $
105 45 85 70 50 90 30 23 100 110 105 95 105 60 110 120 95 90 60 70Explanation / Answer
a. Enter data in Minitab-Stat-Basic Statistics-Display Descriptive Statistics-type C1 in Variables-click OK. The session window display the sample statistics.
xbar=$80.90, s=$28.29
b. Assume prices of summer sleeping bags is normally distributed, population standard deviation is unknown. Use Student's t distribution to compute the confidence interval for 1-population mean.
The 90% c.i for the mean price mu of all summer bags is:xbar+-talpha/2, df=n-1 (s/sqrt n), where, xbar is sample mean, talpha/2, df=n-1 is the t critical value at alpha/2 (alpha=0.10) and n-1=20-1=19 degrees of freedom, s is sample standard deviation, and n is sample size.
=80.90+-1.729(28.29/sqrt 20)
=(69.96, 91.84)
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