Question

An article presents a study of the failure pressures of roof panels. Following are the failure pressures, in kPa, for five panels constructed with 6d smooth shank nails. These data are consistent with means and standard deviations presented in the article. 3.32 2.52 3.45 2.38 3.01 Find a 95% confidence interval for the mean failure pressure for this type of roof panel. Round the answers to three decimal places. The 95% confidence interval is ( , ).

Answer 1

From the data: = 2.936 kPa, s = 0.4742 Kpa

Since population standard deviation is unknown, we use t critical values.

The tcritical (2 tail) for = 0.05, for df = n -1 = 4, is 2.7764

The Confidence Interval is given by ME, where

The Lower Limit = 2.936 - 0.5887 = 2.3472      2.347    (Rounding to 3 decimal places)

The Upper Limit = 2.936 + 0.5887 = 3.5248       3.525     (Rounding to 3 decimal places)

The 95% Confidence Interval is (2.347 , 3.525)

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Calculation of mean and standard deviation of the sample

Mean = Sum of Observations/Total Observations

Standard Deviation = Sqrt(Variance), where Variance = Sum of Squares/(n - 1)

#	X	Mean	(x - mean)2
1	3.32	2.936	0.147456
2	2.52	2.936	0.173056
3	3.45	2.936	0.264196
4	2.38	2.936	0.309136
5	3.01	2.936	0.005476
Total	14.68		0.89932

n	5
Sum	14.68
Average	2.936
SS(Sum of squares)	0.89932
Variance = SS/n-1	0.225
Std Dev=Sqrt(Variance)	0.4742

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