Question

Young men in North America and Europe, but not in Asia, tend to think they need more muscle to be attractive. One study presented 200200 young American men with 100100 images of men with various levels of muscle. Researchers measure level of muscle in kilograms per square meter (kg/m2kg/m2) of fat‑free body mass. Typical young men have about 20 kg/m2.20 kg/m2. Each subject chose two images, one that represented his own level of body muscle and one that he thought represented what women prefer.

The mean gap between self‑image and what women prefer was 2.35 kg/m2.2.35 kg/m2.

Suppose that the muscle gap in the population of all young men has a normal distribution with standard deviation 2.5 kg/m2.2.5 kg/m2. If young men thought that their own level of muscle was about what women prefer, the mean muscle gap in the study would be 0.0. We suspect (before seeing the data) that young men think women prefer more muscle than they themselves have.

(a) Select the correct null and alternative hypotheses for testing this suspicion.

?0:?=0H0:μ=0 vs. ??:?≠0Ha:μ≠0

?0:?=0H0:μ=0 vs. ??:?<0Ha:μ<0

?0:?=0H0:μ=0 vs. ??:?>0Ha:μ>0

?0:?=2.35H0:μ=2.35 vs. ??:?>2.35Ha:μ>2.35

(b) What is the value of the test statistic ??z? (Enter your answer rounded to two decimal places.)

?=z=

(c) You can tell just from the value of ?z that the evidence in favor of the alternative is very strong. That is, the ?P‑value is very small. Select the statement that correctly explains why this is true.

Because large values of the statistic show that the data is not consistent with the null hypothesis.

Because large values of the statistic show that the observed result would be likely to occur if the alternative hypothesis were true.

Because large values of the statistic show that the observed result would be unlikely to occur if the null hypothesis were true.

Because large values of the statistic show that the data is consistent with the null hypothesis.

Answer 1

using excel>addin>phstat>one sample test

we have

z Test for Hypothesis of the Mean
Data
Null Hypothesis                m=	0
Level of Significance	0.05
Sample Size	200
Sample Mean	2.35
Population Standard Deviation	2.5
Intermediate Calculations
Standard Error of the Mean	0.1768
Degrees of Freedom	199
z Test Statistic	13.2936
Two-Tail Test
Lower Critical Value	-1.9720
Upper Critical Value	1.9720
p-Value	0.0000
Reject the null hypothesis

(a) Select the correct null and alternative hypotheses for testing this suspicion.

?0:?=0

Ha:μ≠0

(b) the value of the test statistic ?

?=13.29

(c) You can tell just from the value of ?z that the evidence in favor of the alternative is very strong. That is, the ?P‑value is very small. Select the statement that correctly explains why this is true.

Because large values of the statistic show that the data is not consistent with the null hypothesis.