4. Construct a 90% confidence interval for the sample mean based on the following data x̄ =145,n=90,o=3.8
We can use the formula for a confidence interval:
CI = x̄ ± z α/2 * (σ/√n)
where:
x̄ = 145 (sample mean)
n = 90 (sample size)
o = 3.8 (population standard deviation)
z α/2 = 1.645 (z-score for a 90% confidence level)
Substituting the values, we get:
CI = 145 ± 1.645 * (3.8/√90)
CI = 145 ± 1.495
The 90% confidence interval for the sample mean is (143.505, 146.495).