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.

Group	Sample size	Mean	StDev
MD	n1 = 6	[?(x)]1 = 10.94	s1 = 3.11
Prof	n2 = 3	[?(x)]2 = 10.8	s2 = 3.4

1)Case 1: Assume that the population standard deviations are unequal, i.e. ?1 ? ?2. What is the standard error of the difference in sample mean [?(x)]1 ? [?(x)]2? i.e. s.e.([?(x)]1?[?(x)]2) = [answer to 4 decimal places]

2)Which of the following options gives the formula for 99% confidence interval for ?1??2? MULTIPLE CHOICE

a)0.14 ±3.75 ×s.e.([?(x)]1?[?(x)]2)

b)0.14 ±1.53 ×s.e.([?(x)]1?[?(x)]2)

c)0.14 ±2.78 ×s.e.([?(x)]1?[?(x)]2)

d)0.14 ±2.13 ×s.e.([?(x)]1?[?(x)]2)

e)0.14 ±4.6 ×s.e.([?(x)]1?[?(x)]2)

3)Are there significant difference between mean testosterone levels of medical doctors and university professors? MULTIPLE CHOICE

a)yes, because [?(x)]1 ? [?(x)]2

b)no, because [?(x)]1 = [?(x)]2

c)yes, because the entire 99% confidence interval for ?1??2 does not contain 0

d)no, because the 99% confidence interval for ?1??2 contains 0

4)Case 2: Now assume that the population standard deviations are equal, i.e. ?1 = ?2. Compute the pooled standard deviation, spooled [answer to 4 decimal places]

5)What is the margin of error of the 99% pooled confidence interval of ?1??2? [answer to 4 decimal places]

Answer 1

Cae I)

Group	Sample Size	Mean	StDev
MD	6	10.94	3.11
Prof	3	10.8	3.4

1)

The standard error of diefference in sample mean is define as,

Where poopled std dev sp is,

2)

The 99% confidence interval is given by,

where t = 3.49 for 99% confidence interval

3)

d) no, because the 99% confidence interval for contains zero. Correct Answer

Case II)

4)

The pooled standard deviation,

5)

The margin of error is,