Question

a random sample of 26 observations is used to estimate the population mean. the sample mean and the sample standard deviation are calculated as 127.5 and 25.60, respectively. assume that the population is normally distributed. (you may find it useful to reference the t table.) a. construct the 95% confidence interval for the population mean. (round final answer to 2 decimal places.)

Answer 1

To construct a 95% confidence interval for the population mean, we use the formula: (sample mean) ± (t critical value) × (sample standard deviation) / √(sample size).

Step-by-step explanation:

To construct a 95% confidence interval for the population mean, we can use the formula:

(sample mean) ± (t critical value) × **(sample standard deviation) / √(sample size) **

Here, the sample mean is 127.5, the sample standard deviation is 25.60, and the sample size is 26. The t critical value for a 95% confidence level with (n-1) degrees of freedom is approximately 2.056 from the t table. Substituting these values into the formula, we get:

127.5 ± 2.056 × (25.60 / √26) = 127.5 ± 9.97

Rounding to 2 decimal places, the 95% confidence interval for the population mean is (117.53, 137.47).