The researchers suggest that there are occupational differences in mean testoste

Question

The researchers suggest that there are occupational differences in mean testosterone level. Medical doctors and university professors are two of the occupational groups for which means and standard deviations are recorded and listed in the following table.

Let us denote:

1: population mean testosterone among medical doctors,

2: population mean testosterone among university professors,

1: population standard deviation of testosterone among medical doctors,

2: population standard deviation of testosterone among university professors.

1. Which of the following options gives the formula for 98% confidence interval for 12?

a. 0.572.92×s.e.(x¯1x¯2)
b. 0.571.34×s.e.(x¯1x¯2)
c.0.571.75×s.e.(x¯1x¯2)
d. 0.572.12×s.e.(x¯1x¯2)
e. 0.572.58×s.e.(x¯1x¯2)

Explanation / Answer

The value of the multiplier of the SE depends on the Degrees of Freedom.
For twopopulation the degrees of freedom is taken n1+n2-2

where ni= the sample size of ith population , i=1,2.

here degrees of freedom will be 8+11-2=17

so, the t for the 98% confidence interval with 17 df is:

2.567

i.e. prob( -2.567 <t<+2.567)=0.95 where t~t17

so, here we choose the option e.

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