The sample mean and standard deviation for the cold cranking amperages of 100 batteries are [latex]\bar{X}[/latex] = 185.5 and s = 5.0. Find an 85% confidence interval for the mean amperage of the batteries.

We must find the point estimate, the standard error, and the critical value. The point estimate is [latex]\bar{X}[/latex] = 185.5. The standard error is [latex]\sigma_{\bar{X}}[/latex], which we approximate with [latex]\sigma_{\bar{X}}[/latex] ≈ [latex]s / \sqrt{n}=0.5[/latex]. To find the critical value for an 85% confidence interval, set 1- α = 0.85 to obtain α = 0.15 and α/2 = 0.075. The critical value is [latex]z_{.075}[/latex], the. z-score that cuts off 7.5% of the area in the right-hand taiL From the z table, we find [latex]z_{.075}[/latex]= 1.44. The margin of error is therefore (1.44)(0.5) = 0.72. So the 85% confidence interval is 185.5 ± 0.72 or, equivalently, ( 184.78, 186.22).

Question 5.3: The sample mean and standard deviation for the cold cranking...

Principles of Statistics for Engineers and Scientists

The sample mean and standard deviation for the cold cranking amperages of 100 batteries are $\bar{X}$ = 185.5 and s = 5.0. Find an 85% confidence interval for the mean amperage of the batteries.

The "Step-by-Step Explanation" refers to a detailed and sequential breakdown of the solution or reasoning behind the answer. This comprehensive explanation walks through each step of the answer, offering you clarity and understanding.
Our explanations are based on the best information we have, but they may not always be right or fit every situation.

The blue check mark means that this solution has been answered and checked by an expert. This guarantees that the final answer is accurate.
Learn more on how we answer questions.

This Question has been Answered.