Question

1. You take a sample of 4 people’s scores on a personality test. Their scores are 13, 16, 12, and 18. You don’t know the population mean or standard deviation. The mean of these scores is 14.75.

1. Use the corrected standard deviation formula to find the population standard deviation. Round to 2 decimal places. (Hint: Draw the chart)

2. Use the population standard deviation from (a) to find the standard error for these for sample. Round to 2 decimal places.

Answer 1

Solution:

Given that,

12, 13, 16, 18

n = 4

The sample mean is = 14.75

a) The population standard deviation is  

= 4 /(x - )²

⁼  4 (12 - 14.75 )²+ (13 - 14.75 )²+ (16 - 14.75 )²+ (18 - 14.75 )²

= 4 (7.5625 + 3.0625 + 1.5625 + 10.5625 )

= 22.75 / 4

= 5.6875

= 2.38

The population standard deviation is 2.38

b) = / n = 2.38 / 4 = 1.19