Question

1. 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.

75	95	55	105	110	115	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 $

2. Do you want to own your own candy store? Wow! With some interest in running your own business and a decent credit rating, you can probably get a bank loan on startup costs for franchises such as Candy Express, The Fudge Company, Karmel Corn, and Rocky Mountain Chocolate Factory. Startup costs (in thousands of dollars) for a random sample of candy stores are given below. Assume that the population of x values has an approximately normal distribution.

96

170

125

99

75

94

116

100

85

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean startup cost x and sample standard deviation s. (Round your answers to one decimal place.)

x =	thousand dollars
s =	thousand dollars

(b) Find a 90% confidence interval for the population average startup costs μ for candy store franchises. (Round your answers to one decimal place.)

lower limit	thousand dollars
upper limit	thousand dollars

Answer 1

1)

a)from excel:

x=average(array)= 86.40

s =stdev(array )=28.15

b)

std error ='sx=s/√n=28.1488524586144/√20=

6.2943

for 90% CI; and 19 df, value of t=		1.729
margin of error E=t*std error    =		10.88
lower bound=sample mean-E =		75.52
Upper bound=sample mean+E =		97.28

2)

a)

x =106.7

s =28.0

b)

for 90% CI; and 8 df, value of t=		1.860
margin of error E=t*std error    =		17.37
lower bound=sample mean-E =		89.3
Upper bound=sample mean+E =		124.0