Answer:
a. The margin of error is 2.29.
b. 19.23 to 23.81
Step-by-step explanation:
The sample size is n=64.
We start by calculating the sample mean and standard deviation with the following formulas:
The sample mean is M=21.52.
The sample standard deviation is s=6.89.
We have to calculate a 99% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
The degrees of freedom for this sample size are:
The t-value for a 99% confidence interval and 63 degrees of freedom is t=2.656.
The margin of error (MOE) can be calculated as:
Then, the lower and upper bounds of the confidence interval are:
LL=M-t \cdot s_M = 21.52-2.29=19.23\\\\UL=M+t \cdot s_M = 21.52+2.29=23.81
The 99% confidence interval for the mean is (19.23, 23.81).