A market surveyor wishes to know how many energy drinks teenagers drink each week. They want to construct a 95% confidence interval for the mean and are assuming that the population standard deviation for the number of energy drinks consumed each week is 0.6. The study found that for a sample of 233 teenagers the mean number of energy drinks consumed per week is 4.1. Construct the desired confidence interval. Round your answers to one decimal place.
Solution:
Confidence Interval for population mean using z distribution
Given,
= 4.1 ....... Sample mean
= 0.6 ........Population standard deviation
n = 233 ....... Sample size
Note that, Population standard deviation() is known..So we use z distribution.
Our aim is to construct 95% confidence interval.
c = 0.95
= 1- c = 1- 0.95 = 0.05
/2 = 0.05 2 = 0.025 and 1- /2 = 0.975
Search the probability 0.975 in the Z table and see corresponding z value
= 1.96 for the 95% Confidence interval
Now , confidence interval for mean() is given by:
4.1 -1.96*(0.6/ 233) 4.1 +1.96*(0.6/ 233)
4.1 - 0.07704232157 < < 4.1 + 0.07704232157
4.0 < < 4.2
is the required 95% confidence interval for mean....
Answer is (4.0,4.2)
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