In a random sample of 7 residents of the state of Montana, the mean waste recycled per person per day was 1.1 pounds with a standard deviation of 0.64 pounds. Determine the 90% confidence interval for the mean waste recycled per person per day for the population of Montana. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Solution :
Given that,
sample size = n = 7
Degrees of freedom = df = n - 1 = 7 - 1 = 6
t_{ /2,df} = 1.943
Margin of error = E = t_{/2,df} * (s /n)
= 1.943 * (0.64 / 7)
= 0.470
The 90% confidence interval estimate of the population mean is,
- E < < + E
1.1 - 0.470 < < 1.1 + 0.470
0.630 < < 1.570
90% confidence interval for the mean : (0.630 , 1.570)
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