8) How much does a sleeping bag cost? Let\'s say you want a sleeping bag that sh

Question

8) How much does a sleeping bag cost? Let's say you want a sleeping bag that should keep you warm in temperatures from 20 to 45°F. A random sample of prices (S) sleeping bags for this temperature range is shown below 80 90 100 120 75 37 30 23 100 110 105 95 105 60 110 120 95 90 60 70 a) Calculate the sample mean and sample standard deviation. b) Calculate 95% confidence interval for the true average price of all sleeping bags of this kind. c) Interpret the confidence interval obtained in above part for this situation. d) Does the interval suggest that $65 is a plausible value for them price? Justify your answer

Explanation / Answer

a)
Mean = 83.75
std. dev. = 28.9662

b)

c)

There is 95% chance that any sample of size 20 will have mean cost within the above calculated confidence interval.

d)

As per confidence interval, 65 is not a plausible value for them

CI for 95% n 20 mean 83.75 z-value of 95% CI 1.9600 std. dev. 28.9661781 SE = std.dev./sqrt(n) 6.47703 ME = z*SE 12.69475 Lower Limit = Mean - ME 71.05525 Upper Limit = Mean + ME 96.44475 95% CI (71.0552 , 96.4448 )

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