Obtain appropriate diagrams and summary statistics to describe the distributions of age, height and gender

Obtain appropriate diagrams and summary statistics to describe the distributions of age, height and gender for the study group. Data descriptions for females should be given separately from those for males. Provide brief commentaries to accompany your diagrams and summary statistics.

2(i) Obtain appropriate diagrams and summary statistics to compare grip strength in the dominant hand with the first measurement of grip strength in the non-dominant hand for females only. Provide a brief commentary to accompany your diagrams and summary statistics, which should focus on the possible difference in magnitude of grip strength between the dominant and non-dominant hand.

2 (ii) Carry out an appropriate statistical test of the null hypothesis that the mean difference in grip strength between the dominant and non-dominant hand for females is zero, against a two-sided alternative hypothesis. What do you conclude?

Solution: (a) Now, we need to test:

\[\begin{aligned} & {{H}_{0}}:{{\mu }_{D}}=0 \\ & {{H}_{A}}:{{\mu }_{D}}\ne 0 \\ \end{aligned}\]

Using Minitab:

The t-statistics is t = 5.07, and the corresponding p-value is p = 0.000, which means that we reject the hypothesis. Hence, we have enough evidence to claim that the mean difference is different from zero.

2(iii) Obtain a 95% confidence interval for the mean difference in grip strength between the dominant and non-dominant hand, for females. Briefly describe how you interpret this confidence interval.

3 (i) Obtain appropriate diagrams and summary statistics to describe the following:

The distribution of the three repeat measurements of grip strength of the non-dominant hand, for males only;
The distribution of the three pairwise differences between measurements (i.e. between measurements 1 and 2, 1 and 3, and 2 and 3), for males only.

(8, 12)

Provide a short commentary to accompany your diagrams and summary statistics, which should focus on any possible tendency for grip strength to increase or decrease over the three repeat measurements.

3 (ii) Carry out a two-factor analysis of variance of grip strength of the non-dominant hand in males, in which the factors are study subject (1 to 11) and repeat measurement (1 to 3). Use the resulting analysis of variance table to carry out a test of the null hypothesis that the mean grip strength does not differ between repeat measurements. What do you conclude?

(10)

3 (iii) From the analysis of variance table, calculate the Intraclass Correlation Coefficient (ICC), using the formula:

\[ICC=\frac{M{{S}_{Subjects}}-M{{S}_{Error}}}{M{{S}_{Subjects}}+2\times M{{S}_{Error}}}\]

where MS _Subjects denotes the Mean Square for Subjects, and MS _Error denotes the Mean Square for Error in the Analysis of Variance table. How do you interpret the value of the ICC in this case?

4 (i) Obtain a scatter diagram showing grip strength of the dominant hand in females (vertical axis) and height (horizontal axis). Provide a brief commentary to accompany your scatter diagram, which should focus on any possible relationship between the two variables.

4 (ii) Carry out a regression analysis, in which grip strength of dominant hand is the dependent (or response) variable, and height is the explanatory (or predictor) variable.

4 (iii) Using the regression output, carry out a test of the null hypothesis that the slope of the regression line in the underlying population is zero, against a two-sided alternative. What do you conclude?

4 (iv) Obtain a 95% confidence interval for the slope of the regression line.

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