Answer: a. 47 plusminus (1.753*(5 ÷ 3.8730)
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 = 5
n = number of samples = 15
z represents the test statistic
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 test statistic score
In order to use the t distribution, we would determine the degree of freedom, df for the sample.
df = n - 1 = 15 - 1 = 14
Since confidence level = 90% = 0.90, α = 1 - CL = 1 – 0.90 = 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 = 1.753
Margin of error = 1.753(5 ÷ 3.8730)
Confidence interval = 47 ± 1.753(5 ÷ 3.8730)
