Constructing Confidence Intervals In Exercises 17-20 YOU ARE GIVEN THE SAMPLE ME

Question

Constructing Confidence Intervals In Exercises 17-20 YOU ARE GIVEN THE SAMPLE MEAN And the sample standard deviation assume the population is normally distributed and the t-distribution to find the margin of error and construct a 95% confidence intervals for the population mean. Interprets the result .if convenient, use technology to construct the confidence interval. 17. commute time in a random sample of eight people , the mean commute time to work was 35.5 minutes and the standard deviation was7.5minutes .

Explanation / Answer

Note that              
Margin of Error E = t(alpha/2) * s / sqrt(n)              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    35.5          
t(alpha/2) = critical t for the confidence interval =    2.364624252          
s = sample standard deviation =    7.5          
n = sample size =    8          
df = n - 1 =    7          
Thus,              

Margin of Error E =    6.270156912   [ANSWER]
      
Lower bound =    29.22984309          
Upper bound =    41.77015691          
              
Thus, the confidence interval is              
              
(   29.22984309   ,   41.77015691   ) [ANSWER]

Hence, we are 95% confident that the true mean commute time to work is between 29.230 and 41.770 minutes. [CONCLUSION]

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