A government agency reports a confidence interval of (26.2, 30.1) when estimatin

Question

A government agency reports a confidence interval of (26.2, 30.1) when estimating the mean commute time (minutes) for the population of workers in a city. Find the estimated margin of error. Find the sample mean. In many real-life situations, the population standard deviation is unknown and it is often not practical to collect samples of size 30 or more. If the random variable is approximately normally distributed, one can use a t-distribution instead of a z-distribution. You randomly select 16 coffee shops and determine the temperature of the coffee sold at each shop. The sample mean temperature is 162.0 degree F with a sample deviation of 10.0 degree F. Construct a 95% confidence interval for the population mean temperature. Assume the temperatures are approximately normally distributed. The following sample data represents the grade point averages of 15 randomly selected college students: Construct a 99% confidence interval for the population mean. Assume the population is normally distributed.

Explanation / Answer

3) CI=[26.2,30.1]

Hence Mean=(26.2+30.1)/2=28.15

ME=(30.1-26.2)/2=1.95

4)n=16,mean=162,stddev=10,Z(0.975)=1.96

standard deviation of mean=10/sqrt(16)=2.5

Hence 95% CI=[162-1.96*2.5,162+1.96*2.5]=[157.1,166.9]

5)n=15,mean=2.3533,stddev=1.0322,Z(0.995)=2.576

standard dev of mean=1.0322/sqrt(15)=0.2665

Hence 99% CI=[2.3533-2.576*0.2665,2.3533+2.576*0.2665]=[1.6668,3.0399]

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