4 John regularly downloads podcasts onto his mobile phone. From past experience he knows that the average time to download one 30 -minute podcast is 12.7 s . He believes that this time has recently increased. At each of 12 randomly chosen times, he downloads a 30-minute podcast. The times in seconds to download the 12 podcasts are as follows.
\(\begin{array} { l l l l l l l l l l l } 12.63 & 13.24 & 11.73 & 14.91 & 13.17 & 13.53 & 12.33 & 14.27 & 11.48 & 13.51 & 13.05 \end{array} 13.83\)
- Given that it is not known whether the times are Normally distributed, carry out a suitable test at the \(5 \%\) significance level to investigate whether the average download time has increased.
- What assumption is required to carry out the test in part (a)?