Question

Each year, all final year students take a mathematics exam. It is hypothesized that the population mean score for this test is 85. It is known that the population standard deviation of test scores is 11. A random sample of 30 students take the exam. The mean score for this group is 100.
Calculate the 95% confidence interval for the population mean test score. Give your answers to 2 decimal places.

Answer 1

Answer:

95% Confidence interval:  (96.06,103.94)

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 85

Sample mean, $\bar{x}$ = 100

Sample size, n = 30

Alpha, α = 0.05

Population standard deviation, σ = 11

95% Confidence interval:

$\mu \pm z_{critical}\frac{\sigma}{\sqrt{n}}$

Putting the values, we get,

$z_{critical}\text{ at}~\alpha_{0.05} = 1.96$

$100 \pm 1.96(\frac{11}{\sqrt{30}} ) = 100 \pm 3.94= (96.06,103.94)$

(96.06,103.94) is the 95% confidence interval for  the population mean test score.