Obesity in adult males is associated with lower levels of sexhormone. A study investigated a possible link between obesity andtestosterone levels in adolescent males between the ages of 14 and20 years. The study compared 25 obese adolescent males and 25adolescent males with a healthy weight. Their plasma testosteroneconcentrations (in nanomoles per liter, nmol/l) are provided:
| Obese adolescentmales |
|---|
| 0.30 | 0.24 | 0.19 | 0.17 | 0.18 | 0.23 | 0.24 | 0.06 | 0.15 |
| 0.17 | 0.18 | 0.17 | 0.15 | 0.12 | 0.25 | 0.25 | 0.25 | 0.32 |
| 0.35 | 0.37 | 0.39 | 0.46 | 0.49 | 0.42 | 0.36 | | |
| Adolescent males with ahealthy weight |
|---|
| 0.78 | 0.70 | 0.63 | 0.60 | 0.60 | 0.69 | 0.76 | 0.58 | 0.50 |
| 0.48 | 0.49 | 0.43 | 0.42 | 0.38 | 0.35 | 0.35 | 0.32 | 0.31 |
| 0.28 | 0.25 | 0.23 | 0.24 | 0.24 | 0.26 | 0.27 | | |
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We suspect that obese adolescent males have a lower plasmatestosterone level, on average. Do the data support thissuspicion?
(a) Select the null and alternative hypotheses.
?0:??=?? versus ??:??
?0:??=?? versus ??:??>?? .
?0:??=?? versus ??:??≠?? .
?0:??=?? versus ??:??≥?? .
Obtain these values. (Enter your answers rounded to threedecimal places.)
?⎯⎯⎯?=
?⎯⎯⎯?=
??=
??=
?=
The test ?‑value is
?>0.05
0.05>?>0.01
?<0.001
0.01>?>0.001
Choose the correct conclusion.
The study found strong, significant evidence that obeseadolescent males have higher testosterone levels, on average, thanadolescent males with a healthy weight.
The study found strong, significant evidence that obeseadolescent males have lower testosterone levels, on average, thanadolescent males with a healthy weight.
The study failed to find evidence that obese adolescent maleshave different testosterone levels, on average, than adolescentmales with a healthy weight.
The study found strong, significant evidence that obeseadolescent males have the same testosterone levels, on average,than adolescent males with a healthy weight.
(b) Give a 95% confidence interval for the difference in meanplasma testoterone level between adolescent males who are obese(?1) and those who have a healthy weight (?2). (Enter your answersrounded to 3 decimal places.)
lower bound:
upper bound:
