Question

Obesity in adult males is associated with lower levels of sex hormone. A study investigated a possible link between obesity and testosterone levels in adolescent males between the ages of 14 and 20 years. The study compared 25 obese adolescent males and 25 adolescent males with a healthy weight. Their plasma testosterone concentrations (in nanomoles per liter, nmol/l) are provided:

Obese adolescent males
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 a healthy 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 plasma testosterone level, on average. Do the data support this suspicion?

(a) Select the null and alternative hypotheses.

?0:??=?? versus ??:??<?? .

?0:??=?? versus ??:??>?? .

?0:??=?? versus ??:??≠?? .

?0:??=?? versus ??:??≥?? .

Obtain these values. (Enter your answers rounded to three decimal 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 obese adolescent males have higher testosterone levels, on average, than adolescent males with a healthy weight.

The study found strong, significant evidence that obese adolescent males have lower testosterone levels, on average, than adolescent males with a healthy weight.

The study failed to find evidence that obese adolescent males have different testosterone levels, on average, than adolescent males with a healthy weight.

The study found strong, significant evidence that obese adolescent 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 mean plasma testoterone level between adolescent males who are obese (?1) and those who have a healthy weight (?2). (Enter your answers rounded to 3 decimal places.)

lower bound:

upper bound:

Answer 1