Introduction to Biostatistics

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Introduction to Biostatistics, autumn
2019
Assignment 2
Due Sunday September 15, 2019
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Question 1
a) The 95% confidence interval for the mean grip strength of the grandparents in
Parramatta was evaluated as [31.09, 32.12]. The 95% CI implied that there is a 95%
chance or probability that population mean grip strength was somewhere between
31.09 kilograms and 32.12 kilograms.
R-Commander Output:
b) Grip strength of 33 kilograms does not lie within the CI, implying significant different
grip strength of grandparents, other 33 kilograms.
Reason: At 5% significance level, the confidence interval of grip strength indicates
that average grip strength of grandparents would be within the range of 31.09
kilograms and 32.12 kilograms (Greenland et al., 2016).
c) Null hypothesis: H0: ( μm =μf ) : Male and female have similar average of grip
strength.
Alternate hypothesis: HA: ( μm ≠μf ) : There is a significant difference between
average grip strength of male and female grandparents.
Level of significance: α = 0.05
Test Statistics: The two sample independent t-test has been used to compare the
average grip strength of male and females.
Grip strength was noted to be normal using Shapiro-Wilk Test (W = 0.992, p =
0.275), and the observations are assumed to be independent
T-value = -3.21 and P-value = 0.0018 < 0.05

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Decision: Null hypothesis rejected at 5% level of significance.
Conclusion: There is a significant difference between average grip strength of male
and female grandparents, where average grip strength of male (M = 30.75)
grandparents was higher compared to and female grandparents (M = 32.40).
R-Commander Output:
d) Null hypothesis: H0: Hand grip strength levels of male and females have identical
distributions.
Alternate hypothesis: HA: Distribution of hand grip strength levels of male and
females have significantly different distributions.
Level of significance: α = 0.05

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Test Statistics: The two sample Wilcoxon test has been used to compare the average
grip strength of male and females.
R commander output: W = 5303, p = 0.004 < 0.05
Decision: Null hypothesis rejected at 5% level of significance.
Conclusion: There is a significant difference between the two distributions of hand
grip strength of male and female grandparents, where males have significantly higher
hand grip strength.
R-Commander Output:
Question 2
a) For one sample proportion test (Chi-square test of independence), observations are
assumed to be identically distributed. The expected values are obviously greater than
5 in this case.
Null hypothesis: H0: Proportion of grandparents with hypertension is less equal to
0.25.
Alternate hypothesis: HA: Proportion of grandparents with hypertension is
significantly greater than 0.25.
Level of significance: α= 0.05
Test Statistics: The one sample Chi-square test has been used to evaluate the
proportion of grandparents with hypertension.
R commander output: Chi-squared = 8.93, df = 1, p-value = 0.001 < 0.05
Decision: Null hypothesis rejected at 5% level of significance.
Conclusion: There is enough statistical evidence that pproportion of grandparents with
hypertension is significantly greater than 0.25.