Question

QUESTION PART A: For a confidence level of 80% with a sample size of 26, find the critical t value.

QUESTION PART B: Assume that a sample is used to estimate a population mean μμ. Find the margin of error M.E. that corresponds to a sample of size 13 with a mean of 46.5 and a standard deviation of 13.3 at a confidence level of 99%.

Report ME accurate to one decimal place because the sample statistics are presented with this accuracy.
M.E. =

Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

Answer 1

A: For a confidence level of 80% with a sample size of 26, the degree of freedom is calculated as n-1=26-1=25

the critical t value is calculated using excel formula =T.INV.2T(0.2,25) which results in t value=1.316.

B: For a  sample of size n=13 with a mean of M=46.5 and a standard deviation of S=13.3 at a confidence level of 99% the margin of error E is calculated as:

=>E=. t* (s_M)

where:
t = t statistic determined by the confidence level and degree of freedom using excel formula. df=n-1
s_M = standard error = √(s²/n)
t = 3.055 calculated using excel formula at df=n-1=13-1=12 , the formula used to find the tc is =T.INV.2T(0.01,12)
s_M = √(13.3²/13) = 3.69

=> t* (s_M)
=> 3.055*3.689
=> 11.3