Construct the indicated confidence interval for the population mean $\mu$ using the t-distribution. c = 0.99, $\bar { x }$ = 22.4, s = 3.8, n = 19
A)(19.9, 24.9)
B)(16.3, 26.9)
C)(17.2, 23.6)
D)(18.7, 24.1)

Question

Quizplus · Accepted Answer

The confidence interval for the population mean using the t-distribution is calculated using the formula: $\bar{x} \pm t_{\alpha/2} \times \frac{s}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $s$ is the sample standard deviation, $n$ is the sample size, and $t_{\alpha/2}$ is the t-score corresponding to the desired confidence level and degrees of freedom (df = n - 1). For a 99% confidence level and 18 degrees of freedom, the t-score (from t-tables or calculators) is approximately 2.878. Plugging in the values: $22.4 \pm 2.878 \times \frac{3.8}{\sqrt{19}}$ gives an interval of approximately (19.9, 24.9).

Construct the Indicated Confidence Interval for the Population Mean μ\muμ Using the T-Distribution

Construct the Indicated Confidence Interval for the Population Mean $\mu$ Using the T-Distribution