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 2.49 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.

Answer 1

Answer:

95% confidence interval: (2.339,3.521)

Step-by-step explanation:

We are given the following in the question:

3.32, 2.49, 3.45, 2.38, 3.01

Formula:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$  

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.  

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$\bar{x} =\displaystyle\frac{14.65}{5} = 2.93$

Sum of squares of differences = 0.925

$\sigma = \sqrt{\frac{0.925}{4}} = 0.48$

95% confidence interval:

$\bar{x} \pm t_{critical}\displaystyle\frac{s}{\sqrt{n}}$  

Putting the values, we get,  

$t_{critical}\text{ at degree of freedom 4 and}~\alpha_{0.05} = \pm 2.77$  

$2.93 \pm 2.77(\frac{0.48}{\sqrt{5}} ) = 2.93 \pm 0.591 = (2.339,3.521)$