business statistics

Question

If n=12, ¯x¯(x-bar)=30, and s=8, construct a confidence interval at a 95% confidence level. Assume the data came from a normally distributed population.

Give your answers to one decimal place.

_______ < μ < _________

Answer 1

hi Salma H.

To construct a confidence interval for the population mean (μ) at a 95% confidence level, you can use the formula for a confidence interval for a normally distributed population:

Confidence Interval = x̄ ± (Z * (s / √n))

Where:

- x̄ (x-bar) is the sample mean.

- Z is the critical value for a 95% confidence level. You can find this value from a standard normal distribution table. For a 95% confidence level, Z ≈ 1.96.

- s is the sample standard deviation.

- n is the sample size.

Given:

- n = 12

- x̄ = 30

- s = 8

Now, calculate the confidence interval:

Confidence Interval = 30 ± (1.96 * (8 / √12))

Confidence Interval ≈ 30 ± (1.96 * (8 / √12))

Confidence Interval ≈ 30 ± (1.96 * (8 / √12))

Confidence Interval ≈ 30 ± (1.96 * (8 / 3.4641))

Confidence Interval ≈ 30 ± (1.96 * 2.3081)

Confidence Interval ≈ 30 ± 4.5183

Now, calculate the lower and upper bounds of the confidence interval:

Lower Bound = 30 - 4.5183 ≈ 25.4817

Upper Bound = 30 + 4.5183 ≈ 34.5183

So, the 95% confidence interval for the population mean μ is approximately:

25.5 < μ < 34.5 (rounded to one decimal place)

I hope this will help. I am happy to tutor you on any other questions you may have; please feel free to shoot me a message!