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 tα2

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:

$$\begin{gathered} \frac{\alpha }{2}=\frac{0.05}{2} \\ =0.025 \end{gathered}$$

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

$$\begin{gathered} df=n-1 \\ =12-1 \\ =11 \end{gathered}$$

Now, the value ofrole="math" localid="1648193070546" $t_{\frac{\alpha }{2}}$for 11 degrees of freedom and 0.025 significance level is equal to 2.201.