edumeister_logo

STA286_Assignment_Report.pdf-pg. 12 Appendix C: Approximation toshowing page 13-14 out of 23

Page 13
pg. 12
Appendix C: Approximation to Normal Distribution
Figure 14: Normal Quantile-Quantile plot for
Typing Time on Laptop Keyboard
Figure 15: Normal Quantile-Quantile plot for
Number of Errors on Laptop Keyboard
Figure 16: Normal Quantile-Quantile plot for
Typing Time on Nexus Keyboard
Figure 17: Normal Quantile-Quantile plot for
Number of Errors on Nexus Keyboard


Page 14
pg. 13
The above quantile-quantile plots show an almost linear relationship between the
standard normal quantiles and sample quantiles. This suggests that the data can also be
approximated as a normal distribution. Although the data fits a lognormal distribution better,
statistical analysis is much simpler using a normal distribution.
To further verify this assumption in a more quantitative fashion, a Shapiro-Wilk test of
normality can be done in R to test the null hypothesis that the data is normally distributed [6].
The P-value returned by the Shapiro-Wilk test is 0.06587 for the typing time on the laptop
keyboard, 0.1346 for the typing time on the Nexus keyboard, 0.1364 for the number of typing
errors made on the laptop keyboard, and 0.07519 for the number of typing errors made on the
Nexus keyboard. Thus, under a test with
5% level of significance, we cannot reject the null
hypothesis being that the data is normally distributed, since the P-values for all four sets of data
are greater than 0.05.
Appendix D: Confidence Intervals
The confidence intervals on the means and the standard deviations for the typing times
and error counts are calculated under assumption that the experimental data is normally
distributed (see Appendix C for discussion). The analysis uses a 95% confidence interval, which
results in an
value of 0.05 for one-sided test.
As the population variances are not known, the confidence interval for the means is
calculated using a Student's t-Distribution, as shown in the formula below [4]
̅ − 
/2
/√
<  < ̅ + 
/2
/√
where
̅
is the sample mean,
/2
is the t-value with
- 1 degrees of freedom that gives an area
of
2
to the right,
is the sample size, and
is the sample variance.
The confidence interval of the standard deviation is calculated using chi-squared distribution, as
shown in the formula below [4]
(−1)
2
2
/2
<
2
<
(−1)
2
2
1−/2
where
is the sample size,
2
is the sample variance, ,
2
/2
and
2
1−/2
are the Chi-squared
values with
−1
degree of freedom that leaves an area of
2
and ,
1− 2
respectively, to
the right.


Upload your course documents to receive views for accessing documents on Edumeister.

Upload documents to earn views.