In: Statistics and Probability
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.
90 | 65 | 110 | 35 | 95 | 50 | 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 | $ |
90 | 9.10 | 82.81 |
65 | -15.90 | 252.81 |
110 | 29.10 | 846.81 |
35 | -45.90 | 2106.81 |
95 | 14.10 | 198.81 |
50 | -30.90 | 954.81 |
30 | -50.90 | 2590.81 |
23 | -57.90 | 3352.41 |
100 | 19.10 | 364.81 |
110 | 29.10 | 846.81 |
105 | 24.10 | 580.81 |
95 | 14.10 | 198.81 |
105 | 24.10 | 580.81 |
60 | -20.90 | 436.81 |
110 | 29.10 | 846.81 |
120 | 39.10 | 1528.81 |
95 | 14.10 | 198.81 |
90 | 9.10 | 82.81 |
60 | -20.90 | 436.81 |
70 | -10.90 | 118.81 |
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Refer t-table or use excel function "=T.INV.2T(0.10,19)" to find the critical value of t.