Answer:
Step-by-step explanation:
Considering the central limit theorem, the distribution is normal since the number of samples is large. Also, the population standard
deviation is known. We would determine the z score.
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.90 = 0.1
α/2 = 0.1/2 = 0.05
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.05 = 0.95
The z score corresponding to the area on the z table is 2.05. Thus, confidence level of 90% is 1.645
Confidence interval is written in the form,
(Sample mean - margin of error, sample mean + margin of error)
The sample mean, x is the point estimate for the population mean.
Confidence interval = mean ± z × σ/√n
Where
σ = population standard Deviation
Confidence interval = x ± z × σ/√n
x = 22.8 hours
σ = 6.4 hours
n = 175
i) Confidence interval = 22.8 ± 1.645 × 6.4/√175
= 22.8 ± 0.80
The lower end of the confidence interval is
22.8 - 0.80 = 22
The upper end of the confidence interval is
22.8 + 0.80 = 23.6
ii) error bound is the same as the margin of error
Error bound = 0.8
