Question

1. The mean scores of a random sample of 17 students who took a special test is 83.5. If the standard deviation of the scores is 4.1, and the sample comes from an approximately normal population, find the interval estimates of the population mean adopting a confidence level of 90%.

Answer 1

$\mu = 83.5 , \sigma =4.1$

$s=\sqrt{\dfrac{\sigma^2}{n}}= \sqrt{\dfrac{(4.1^2)}{17}} ​ = 0.99$

$\alpha=0.1,z_{\frac{\alpha}{2}}=1.645$

Interval estimates is-

$= \mu ± Z\times s \\ = 83.5 ± 1.645 \times 0.99\\ = 83.5 ± 1 .628$