The time to failure of 18 batteries was measured. The average time to failure of

Question

The time to failure of 18 batteries was measured. The average time to failure of the 12 batteries is 22.81 hours and the standard deviation of the 12 batteries is 1.55 hours. The population is assumed to be normally distributed. Determine a 95% confidence interval for mu. An election is to take place next week. A poll is taken to help determine the chances of winning the election. The poll asks 1150 randomly selected voters their choice in the election. Of those surveyed, 620 say that they will vote for our candidate. Determine a 95% confidence interval to determine the true proportion that will vote for our candidate.

Explanation / Answer

Q1.

Confidence Interval
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=22.81
Standard deviation( sd )=1.55
Sample Size(n)=12
Confidence Interval = [ 22.81 ± t a/2 ( 1.55/ Sqrt ( 12) ) ]
= [ 22.81 - 2.201 * (0.447) , 22.81 + 2.201 * (0.447) ]
= [ 21.825,23.795 ]
Interpretations:
1) We are 95% sure that the interval [21.825 , 23.795 ] contains the true population mean
2) If a large number of samples are collected, and a confidence interval is created
for each sample, 95% of these intervals will contains the true population mean  

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