You go to a store, buy 9 digital thermometers, put them all on the ground togeth

Question

You go to a store, buy 9 digital thermometers, put them all on the ground together in the shade, and record the temperature of each. The summary results of the sample were x = 11.8 and s = .45 degrees Fahrenheit.

a) Find a 95% confidence interval for the (population) average temperature of thermometers of this brand (on this day at this time) if we assume the temperatures are normally distributed.

b) What does your interval mean in the context of the problem?

c) Find a 95% confidence interval for the (population) average temperature of thermometers of this brand (on this day at this time) if we assume the temperatures are normally distributed and the population standard deviation is known as (sigma) = .45.

d) Would a 99% confidence interval calculated from the same data be narrower or wider than the 95% interval? Explain.

Explanation / Answer

Ans:

a)Here,population standard deviation is unknown,so use t-distribution.

df=9-1=8

t value for 95% CI is 2.306

95% CI for population mean

=11.8+/-2.306*0.45/sqrt(9)

=11.8+/-0.35

=(11.45,12.15)

b)if we take number of samples from the population,there is 95% chance that population mean will contained within above limits.

c)As,population standard deviation is known,we can use normal distribution.

z value for 95% CI is 1.96

95% confidence interva; for population mean

=11.8+/-1.96*0.45/sqrt(9)

=11.8+/-0.29

=(11.51,12.09)

d)As,z or t multiplier increases with increase in confidence level,so 99% confidence interval will be wider than 95% confidence interval.

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