Answer:
Step-by-step explanation:
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.
Margin of error = z × s/√n
Where
s = sample standard deviation = 0.0074
n = number of samples = 27
From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score
In order to use the t distribution, we would determine the degree of freedom, df for the sample.
df = n - 1 = 27 - 1 = 26
Since confidence level = 90% = 0.90, α = 1 - CL = 1 – 0.9 = 0.1
α/2 = 0.1/2 = 0.05
the area to the right of z0.05 is 0.05 and the area to the left of z0.05 is 1 - 0.05 = 0.95
Looking at the t distribution table,
z = 1.706
The critical value is 1.706
Margin of error = 1.706 × 0.0074√27
= 0.0024
The 90% confidence interval is
0.097 ± 0.0024
