You took a random sample of 18 twoslice toasters and found t

You took a random sample of 18 two-slice toasters and found the mean price was $54.95. The population standard deviation was $17.26. Assume the prices are normally distributed. Find the 90% confidence interval for the population mean. Explain why you are using either the z distribution or thr t distribution.

Please explain how you get answer, thanks

Solution

a)
Here, population stanadard deviation is known so, we
use z -test in such case
b)
CI = x ± Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=54.95
Standard deviation( sd )=17.26
Sample Size(n)=18
Confidence Interval = [ 54.95 ± Z a/2 ( 17.26/ Sqrt ( 18) ) ]
= [ 54.95 - 1.64 * (4.068) , 54.95 + 1.64 * (4.068) ]
= [ 48.278,61.622 ]