t.test vs hand calc confidence intervals discrepency

General
#1

Hi Guys,

Thank you in advance. Could anyone explain why my lecturers calculation for 99% confidence intervals

Screenshot 2021-11-22 at 23.49.38
Screenshot 2021-11-22 at 23.49.381204×708 34.4 KB

Does not equate to R's function:

t.test(study$Questions, conf.level = 0.99)

Which gives:

data:  study$Questions
t = 78.112, df = 122, p-value < 2.2e-16
alternative hypothesis: true mean is not equal to 0
99 percent confidence interval:
 47.36637 50.64989
sample estimates:
mean of x 
 49.00813

Any help on this matter greatly appreciated!

#2

Your instructor used the normal distribution rather than the t-distribution.

#3

Hi,

Thanks for your response, so knowing that is there a shorter way to calculate the confidence intervals using normal distribution similar to that of the t distribution?

#4

Not sure, but see if z.test() does what you need.