Before any order is shipped, inspectors at Alvarez Manufacturing test a sample of finished units for breaking strength.You select a simple random sample of 49 units from a recently completed order and find that the sample average breaking strength is 814 pounds.Assume that the standard deviation of the breaking strengths for the population of units in the order is known to be 35 pounds.Construct a 95% confidence interval estimate of the average breaking strength you could expect to find if all the units in the order were tested.Report the upper bound for your interval.
A)761.2
B)643.9
C)823.8
D)797.6
E)866.7

Question

Quizplus · Accepted Answer

823.8To construct a 95% confidence interval for the population mean, we use the formula: $\bar{x} \pm Z \frac{\sigma}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $Z$ is the Z-score corresponding to the confidence level, $\sigma$ is the population standard deviation, and $n$ is the sample size. Given $\bar{x} = 814$, $\sigma = 35$, and $n = 49$, and knowing that the Z-score for a 95% confidence level is approximately 1.96, we calculate the margin of error as $1.96 \times \frac{35}{\sqrt{49}} = 1.96 \times 5 = 9.8$. Therefore, the upper bound of the confidence interval is $814 + 9.8 = 823.8$.

Before Any Order Is Shipped, Inspectors at Alvarez Manufacturing Test