D.28 Answers: Tests for two means
Answers to exercises in Sect. 30.12.
Answer to Exercise 30.1:
H0: μS−μNS=0 and H1: μS−μNS≠0.
From output: t=5.478 and P<0.001.
Very strong evidence to support H1.
Answer to Exercise 30.2:
1. Table D.7.
2. H0: μC−μSO=0 and H1: μC−μSO≠0.
Then t=((51−56)−0)/3.3044=−1.513;
P-value larger than 5%.
Sample size are small; test may not be statistically valid.
3. H0: μC−μSO=0 and H1: μC−μSO≠0.
Then t=((36−47)−0)/4.0689=−2.70;
P-value smaller than 5%.
Sample size are small; the test may not be statistically valid.
Conventional | Special Operations | |
---|---|---|
Sample size | 11 | 11 |
Grip strength (in kg) | ||
Mean | 51 | 56 |
Standard deviation | 8 | 9 |
Standard error | 1.86 | 2.71 |
Push-ups (per minute) | ||
Mean | 36 | 47 |
Standard deviation | 10 | 11 |
Standard error | 2.36 | 3.3 |
Answer to Exercise 30.3: H0: μM−μF=0 and H1: μM−μF≠0. From output, t=−2.285; (two-tailed) P-value is 0.024 Moderate evidence to support H1: Moderate evidence (P=0.024) that the mean internal body temperature is different for females (mean: 36.886∘C) and males (mean: 36.725∘C).
The difference between the means, of 0.16 of a degree, is hardly of any practical importance in everyday use.
Answer to Exercise 30.4:
1. H0: The means are equal: μI=μNI or μI−μNI=0.
H1: The means are not equal: μI≠μNI or μI−μNI≠0.
2. CI from -22.54 to -11.95:
the mean sugar consumption
between 11.95 and 22.54 kg/person/year greater
in industrialised countries.
3. Very strong evidence in the sample (P<0.001) that the
mean annual sugar consumption per person is different
for industrialised (mean: 41.8 kg/person/year)
and non-industrialised (mean: 24.6 kg/person/year) countries
(95% CI for the difference 11.95 to 22.54).