Question

Critical Value Refer to Exercise 7 “Requirements” and assume that the requirements are satisfied. Find the critical value that would be used for constructing a 95% confidence interval estimate of \(\mu \) using the t distribution.

Short answer

The critical value for computing the 95% confidence interval estimate of the mean voltage level is equal to 2.201.

Step-by-step solution

Given information

Referring to Exercise 7 CQQ, a sample of size (n) equal to 12 smartphone batteries is considered to estimate the mean voltage level. The confidence level is given to be equal to 95%.

Value of \({t_{\frac{\alpha }{2}}}\)

The confidence level is given to be equal to 95%. Thus, the level of significance \(\left( \alpha \right)\) is equal to 0.05.

Now, the level of significance corresponding to the t-value is computed below:

\(\begin{array}{c}\frac{\alpha }{2} = \frac{{0.05}}{2}\\ = 0.025\end{array}\)

The value of the degrees of freedom is is calculated in the following manner:

\(\begin{array}{c}df = n - 1\\ = 12 - 1\\ = 11\end{array}\)

Now, the value of\({t_{\frac{\alpha }{2}}}\)for 11 degrees of freedom and 0.025 significance level is equal to 2.201.