09 Sept 2021

Posted on:

12 Aug 2021

0

# Statistic(Population variance unknown)

In the below dataset , in the task three solution, how is t statistic calculated as 3.36... Please can you explain. I did not get...

Dataset
\$        78,000 Task 1: Mean \$      92,533
\$        90,000 St. deviation \$      13,932
\$        75,000 Standard error \$        4,644
\$      117,000
\$      105,000 Task 2: Population variance is unknown
\$        96,000 We have a small sample
\$        89,500 We assume that the population is normally distributed
\$      102,300 The appropriate statistic to use is the t-statistic
\$        80,000
Task 3: 99% CI, t8,0.005 3.36
Sample size is 9 => the degrees of freedom are 8.
Instructor
Posted on:

09 Sept 2021

0

Hello Smriti!

Here you have a sample size of 9 observations which means the degrees of freedom would be equal to n-1 or 8.
You use the t-table:

d.f. / α 0.1 0.05 0.025 0.01 0.005
1 3.078 6.314 12.706 31.821 63.657
2 1.886 2.920 4.303 6.965 9.925
3 1.638 2.353 3.182 4.541 5.841
4 1.533 2.132 2.776 3.747 4.604
5 1.476 2.015 2.571 3.365 4.032
6 1.440 1.943 2.447 3.143 3.707
7 1.415 1.895 2.365 2.998 3.499
8 1.397 1.860 2.306 2.896 3.355
9 1.383 1.833 2.262 2.821 3.250

And examine the case for 99% confidence level. This means that half of alpha would be equal to  0.005 (two-sided test).

You check in the table to see that the corresponding value is equal to 3.36.

Best,
The 365 Team