Question

1. Find the 90% Cl for the population mean if sample

mean= 12, SD=2.3 and sample size is 65.
2. Find the 88% Cl for the population mean if sample
mean=23, SD=12, and sample size is 45.
3. Interpret #1 and #1.

Answer 1

The answer is below

Explanation:

1)

mean (μ) = 12, SD(σ) = 2.3, sample size (n) = 65

Given that the confidence level (c) = 90% = 0.9

α = 1 - c = 0.1

α/2 = 0.05

The z score of α/2 is the same as the z score of 0.45 (0.5 - 0.05) which is equal to 1.65

The margin of error (E) is given as:

`E=Z_{(\alpha)/(2) }*(\sigma)/(√(n) ) =1.65*(2.3)/(√(65) ) =0.47`

The confidence interval = μ ± E = 12 ± 0.47 = (11.53, 12.47)

2)

mean (μ) = 23, SD(σ) = 12, sample size (n) = 45

Given that the confidence level (c) = 88% = 0.88

α = 1 - c = 0.12

α/2 = 0.06

The z score of α/2 is the same as the z score of 0.44 (0.5 - 0.06) which is equal to 1.56

The margin of error (E) is given as:

`E=Z_{(\alpha)/(2) }*(\sigma)/(√(n) ) =1.56*(12)/(√(45) ) =2.8`

The confidence interval = μ ± E = 23 ± 2.8 = (22.2, 25.8)