*Please show work for all problems!* The researchers suggest that there are occu
ID: 3366978 • Letter: #
Question
*Please show work for all problems!*
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.
Case 1: Assume that the population standard deviations are unequal, i.e. ?1 ? ?2.
1. 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 95% confidence interval for ?1??2?
?0.06 ±5.84 ×s.e.([?(x)]1?[?(x)]2)
?0.06 ±4.54 ×s.e.([?(x)]1?[?(x)]2)
?0.06 ±2.35 ×s.e.([?(x)]1?[?(x)]2)
?0.06 ±3.18 ×s.e.([?(x)]1?[?(x)]2)
?0.06 ±1.64 ×s.e.([?(x)]1?[?(x)]2)
3. Are there significant difference between mean testosterone levels of medical doctors and university professors?
no, because [?(x)]1 = [?(x)]2
yes, because [?(x)]1 ? [?(x)]2
no, because the 95% confidence interval for ?1??2 contains 0
yes, because the entire 95% confidence interval for ?1??2 does not contain 0
Case 2: Now assume that the population standard deviations are equal, i.e. ?1 = ?2.
4. Compute the pooled standard deviation, spooled [answer to 4 decimal places]
5. Which of the following options gives the formula for 95% confidence interval for ?1??2 for pooled situation?
?0.06 ±1.34 ×1.9265
?0.06 ±2.58 ×1.9265
?0.06 ±2.12 ×1.9265
?0.06 ±2.92 ×1.9265
?0.06 ±1.75 ×1.9265
6. What is the margin of error of the 95% pooled confidence interval of ?1??2? [answer to 4 decimal places]
Group Sample size Mean StDev MD n1 = 3 [?(x)]1 = 10.02 s1 = 3.35 Prof n2 = 15 [?(x)]2 = 10.08 s2 = 3Explanation / Answer
Answer:
1: population mean testosterone among medical doctors=10.02
2: population mean testosterone among university professors=10.08
3: population standard deviation of testosterone among medical doctors=3.35
4: population standard deviation of testosterone among university professors=3
2. Which of the following options gives the formula for 95% confidence interval for ?1??2?
?0.06 ±5.84 ×s.e.([?(x)]1?[?(x)]2)
?0.06 ±4.54 ×s.e.([?(x)]1?[?(x)]2)
?0.06 ±2.35 ×s.e.([?(x)]1?[?(x)]2)
?0.06 ±3.18 ×s.e.([?(x)]1?[?(x)]2)
?0.06 ±1.64 ×s.e.([?(x)]1?[?(x)]2)
Option ?0.06 ±2.35×s.e.([?(x)]1?[?(x)]2) is correct.
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