According to Expediacom workers in Italy lead the world in p

According to Expedia.com, workers in Italy lead the world in paid vacation days, averaging 42 days per year. The following data show the number of paid vacation days for a random sample of 20 Italian workers. These data can also be found in the Excel file titled paid Construct a 95% confidence interval to estimate the average number of paid vacation days for Italian workers. Do the results from this sample validate Fxpedia.com\'s findings? Verify this interval using Excel. What assumptions need to be made about this population?

Solution

A)

Note that              
              
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 =    40.15          
t(alpha/2) = critical t for the confidence interval =    2.093024054          
s = sample standard deviation =    15.89198739          
n = sample size =    20          
df = n - 1 =    19          
Thus,              
              
Lower bound =    32.71232096          
Upper bound =    47.58767904          
              
Thus, the confidence interval is              
              
(   32.71232096   ,   47.58767904   ) [ANSWER]

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b)

YES, becasue 42 is inside this interval.

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c)

Note that              
              
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 =    40.15          
t(alpha/2) = critical t for the confidence interval =    2.093024054          
s = sample standard deviation =    15.89198739          
n = sample size =    20          
df = n - 1 =    19          
Thus,              
              
Lower bound =    32.71232096          
Upper bound =    47.58767904          
              
Thus, the confidence interval is              
              
(   32.71232096   ,   47.58767904   ) [ANSWER]

(I actually did some parts in part a using Excel).

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d)

We need to assume that at the population from where this sample came from is approximately normally distributed.