Hypothesis Testing and Confidence Intervals for Grandparent Carers in Parramatta

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Assignment 2

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Abbreviations:
I. Grip Strength: GS
II. Confidence Interval: CI
III. Dominant: DMN
IV. Non-Dominant: NDMN
Question 1: Answers
a) Method: The 95% CI for GS of grandparent carers in Parramatta has been calculated in
R commander window using one sample t-test.
The 95% CI was identified from the R-output as [31.27, 32.23]. The CI implies that
there is 95% chance that average GS of grandparents will be somewhere between 31.27
kg and 32.23 kg.
b) At 5% level of significance 33 kg GS is significantly different from the estimated GS.
Reason is that GS of 33 kg is outside the 95% confidence interval.
c) Hypothesis testing by independent sample t-test
Step1:
Null hypothesis: There is no difference between averages of GS between male and
females.
Alternate hypothesis: There is significant difference between averages of GS between
male and females (two tailed).
Step 2:
Significance level: 5% => α =0 . 05
Test Selection: According to Shapiro-Wilk test, GS is normally distributed (W = 0.99, p
= 0.96). According to Levene’s test there is no statistical difference between variances
of GS between male and females (F (1, 231) = 1.92, p = 0.17). Therefore, parametric
test is applicable here. Here, a two sample independent t-test has been used.

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Figure 1: Side-by-side box plots for grip strength
Step 3:
Decision Statute:
The test statistic and the p-value are found. If the p-value is less than α =0 . 05 then
null hypothesis will be rejected. Otherwise, the null hypothesis will fail to get rejected.
Step 4:
R Commander Output:
The statistics: t = 1.12, df = 217.73, p-value = 0.265, 95% CI: [-0.42, 1.52]
Step 5:
Conclusion: Null hypothesis failed to get rejected as p-value > 0.05.
Hence, there is no statistically significant difference between average GS of males and
females.

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d) Hypothesis testing by two sample Wilcoxon test
Step1:
Null hypothesis: There is no difference between medians of GS between male and
females.
Alternate hypothesis: There is significant difference between medians of GS between
male and females (two tailed).
Step 2:
Significance level: 5% => α =0 . 05
Test Selection: A non-parametric alternate to independent sample t-test is Wilcoxon test
(also known as Mann Whitney U test).
Step 3:
Decision Statute:
The test statistic and the p-value are found. If the p-value is less than α =0 . 05 then
null hypothesis will be rejected. Otherwise, the null hypothesis will fail to get rejected.
Step 4:
R Commander Output:
The statistics: W = 7401, p-value = 0.216
Step 5:
Conclusion: Null hypothesis failed to get rejected as p-value > 0.05.
Hence, there is no statistically significant difference between medians of GS between
males and females.