In a random sample of 15 mortgage institutions.
Sample size = n = 15
The mean interest rate was 3.57% and the sample standard deviation was 0.36%
Sample mean = x = 3.57%
Sample standard deviation = s = 0.36%
a) construct a 95% confidence interval using the Z or T Interval
The 95% confidence interval is given by
Where tα/2 is the t-value, from the t-table, the t-value at 95% confidence level and 14 degree of freedom (15 - 1 = 14)
tα/2 = 2.145
Therefore, the 95% confidence interval using t-interval is (3.37%, 3.77%)
b) state which interval was used - Z or T Interval
Since the population standard deviation was unknown, and the population was normally distributed hence t-interval was used.
c) interpret your answer in the context of the problem
The 95% confidence interval (3.37%, 3.77%) means that we are 95% confident that the mean interest rate will lie between this interval (3.37%, 3.77%)
It can be as low as 3.37% or as high as 3.77% with 95% confidence