Can anyone help me with my Statistics problem?
Suppose a manager wants to estimate the mean time required for a machine to produce a widget. A random sample of 36 widgets required an average time of 1.5 minutes. The standard deviation for this sample was .30 minutes.
(a) We can assume that distribution of sample means in normal. Why?
(b) Construct a 95% confidence interval to estimate the true mean production time for this machine.
Thank you for all your help! You are a life saver!
a) Our sample size n is greater than 30.
b) Use the formula:
x bar +_ E, where E = t* s/sqrt(n) where
x bar = 1.5, s = 0.3, and n = 36
We use Student t distribution because we do not the standard deviation of the population. For 95% confidence level, t = 2.03
So,
1.5 +_ (2.03)(0.3)/sqrt(36) = (1.3985, 1.6015)
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