D.28 Answers: Tests for two means

Answers to exercises in Sect. 30.12.

Answer to Exercise 30.1: H0: μSμNS=0 and H1: μSμNS0. 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: μCμSO=0 and H1: μCμSO0. Then t=((5156)0)/3.3044=1.513; P-value larger than 5%. Sample size are small; test may not be statistically valid. 3. H0: μCμSO=0 and H1: μCμSO0. Then t=((3647)0)/4.0689=2.70; P-value smaller than 5%. Sample size are small; the test may not be statistically valid.
TABLE D.7: The physical profile of conventional and special operation paramedics in Western Australia
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: μMμF=0 and H1: μMμF0. 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: 36.886C) and males (mean: 36.725C).

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 μIμNI=0. H1: The means are not equal: μIμNI or μIμNI0. 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).