Question

A sample of 22 test-tubes tested for number of times they can be heated on a Bunsen burner before they crack is given below. Assume the counts are normally distributed. Use Excel to construct a 99% confidence interval for μ. Round your answers to two decimal places and use increasing order.

Answer 1

To construct a 99% confidence interval for the population mean μ, use the formula: x ± zα/2 * σ/√n. Given the sample size and the normal distribution assumption, find the critical value zα/2 using Excel. Calculate the interval by plugging in the values into the formula.

Step-by-step explanation:

To construct a 99% confidence interval for the population mean μ, we can use the formula: x ± zα/2 * σ/√n, where x is the sample mean, α is the significance level (1 − confidence level), zα/2 is the critical value, σ is the population standard deviation, and n is the sample size.

Given that the sample size is 22 and the counts are normally distributed, we can use Excel to find the critical value zα/2. Using the NORM.S.INV function with a probability of (1 − confidence level)/2, we can find that zα/2 = NORM.S.INV(0.005) = -2.58 (rounded to two decimal places).

Now, we can calculate the confidence interval: x ± zα/2 * σ/√n = x ± (-2.58) * s/√22. Round the results to two decimal places and arrange them in increasing order.

Therefore, the 99% confidence interval for μ is (-2.58, -1.13).