Hypothesis Testing and Confidence Intervals in Biostatistics

Introduction to Biostatistics
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Answer 1
a) The 95% confidence interval for average “grip strength” (kilograms) of grandparent
population in Parramatta is evaluated as [31.27, 32.30]. The confidence interval
implies that there is 95% chance or probability that average “grip strength” of
grandparents in Parramatta will be somewhere between 31.27 kilograms and 32.30
kilograms (Greenland et. al., 2016).
b) The 95% confidence interval of [31.27, 32.30] does not contain “grip strength” of 33
kilograms. Hence, at significance level of 5%, average “grip strength” of 33
kilograms is significantly out of the range of confidence interval. Hence, it can be
inferred that at 5% level, average “grip strength” of grandparents in Parramatta is
significantly different from 33 kilograms.
c) Hypothesis testing for difference in average “grip strength” of males and females:
Step 1:
Null hypothesis: Average “grip strength” of male and female
grandparents in Parramatta is equal.
Alternate hypothesis: There is significant difference between average
“grip strength” of male and female grandparents in Parramatta (two-
tailed).
Significance Level: 5%
Step 2:
Choice of test: Independent sample t-test
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Step 3:
Decision Rule: Observation count n = 233, significance: α =0 . 05
“Grip strength” of grandparents is tested to be a normally distributed
variable. Shapiro-Wilk test indicated the normality of the variable (W =
0.99, P = 0.64). “Grip strength” of males (W = 0.99, p = 0.77) and
females (W = 0.99, p = 0.67) are also normally distributed. The
histograms below presents the distribution of “grip strength” based on
sex of the grandparents.
The Levene’s test revealed homogeneity of variances between male and
female “grip strength” (F = 0.25, p = 0.62). The R commander has been
used to run the independent sample t-test with equal variances. The null
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hypothesis will be rejected if p-value is less than 0.05. Otherwise, the
null hypothesis will get failed to be rejected.
Step 4:
Calculation of Test Statistics: The t-test statistics is evaluated in R
commander. The calculated statistics are: t = - 1.08, p = 0.283, 95% CI
for differences between average “grip strength” = [- 1.59, 0.47].
Step 5:
Conclusion: The p-value is greater than 0.05, which implies that there is
not enough statistical evidence to reject the null hypothesis. Therefore, at
5% level average “grip strength” of males (M = 31.49, SD = 4.09) and
that of the females (M = 32.06, SD = 3.90) are statistically equal.
d) Hypothesis testing with non-parametric test for difference in average “grip strength”
of males and females.
Step 1:
Null hypothesis: Median “grip strength” of male and female
grandparents in Parramatta is equal.
Alternate hypothesis: There is significant difference between Median
“grip strength” of male and female grandparents in Parramatta (two-
tailed).
Significance Level: 5%
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