Question

Part # 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.

80 115 110 55 40 70 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 $

Part # 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.

100 177 129 91 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 =

s =

(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

upper limit

Part #3

What percentage of hospitals provide at least some charity care? Based on a random sample of hospital reports from eastern states, the following information is obtained (units in percentage of hospitals providing at least some charity care):

57 55.9 52.6 65.7 59.0 64.7 70.1 64.7 53.5 78.2

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 percentage x and the sample standard deviation s. (Round your answers to one decimal place.)

x =

s =

(b) Find a 90% confidence interval for the population average μ of the percentage of hospitals providing at least some charity care. (Round your answers to one decimal place.)

lower limit

upper limit

Answer 1

##Part(1)

(a)   {80, 115, 110, 55, 40, 70, 30, 23, 100, 110, 105, 95, 105, 60, 110, 120, 95, 90, 60, 70}, n=20

Sample mean:

Sample standard deviation:

The sample mean, and sample standard deviation,

(b)   90% confidence interval for mean population prices of summer bags,

The formula to calculate confidence interval is:  

At 90% CI, , s=29.56, n=20

Lower limit:

Upper limit:

The 90% confidence interval contains the true population mean prices for summer bags,

##Part(2)

{100, 177, 129, 91, 75, 94, 116, 100, 85}, n=9

(a) Using the formula in part (a) we can calculate the sample mean and standard deviation for this set also or using a calculator easily.

Sample mean,

Sample standard deviation,

(b) 90% confidence interval for

s= 30.61, n=9,

Lower limit:

Upper Limit:

The 90% confidence interval contains the population average startup costs μ for candy store franchises,

##Part(3)

(a) {57 55.9 52.6 65.7 59.0 64.7 70.1 64.7 53.5 78.2} , n=10

Sample mean,

Sample standard deviation,

(b) The 90% confidence interval for population average , percentage providing some charity.

,

Lower limit:

Upper limit:

The 90% confidence interval contains the the population average μ of the percentage of hospitals providing at least some charity care,