Question

Construct a 90% confidence interval for the population mean. Assume that the population has a normal distribution. \begin{aligned} \mathrm{n}=30, \overline{\mathrm{x}}=80.7, \mathrm{~s}=

Answer 1

To construct a 90% confidence interval for the population mean, we need to calculate the error bound using the sample mean, sample size, and sample standard deviation. We can estimate the error bound using the t-distribution and the critical value. Then, we can use the error bound to calculate the confidence interval.

Step-by-step explanation:

To construct a 90% confidence interval for the population mean, we can use the formula:

(x - EBM, x + EBM)

Given that the sample mean (x) is 80.7 and the sample size (n) is 30, we need to calculate the error bound (EBM). Since the population standard deviation (s) is not provided, we cannot directly compute the EBM. However, we can estimate it using the sample standard deviation (s) and the t-distribution.

Therefore, first, we need to determine the critical value (t*) from the t-distribution with n-1 degrees of freedom and a confidence level of 90%. Once we have the critical value, we can calculate the EBM using the formula:

EBM = t* * (s / sqrt(n))

Finally, we can substitute the values into the formula to calculate the confidence interval for the population mean.