Example 7.25

EXAMPLE 7.25

Justin Sullivan/Staff/Getty Images

Length of audio files on an iPod. Table 7.5 presents data on the length (in seconds) of audio files found on an iPod. There was a total of 10,003 audio files, and 50 files were randomly selected using the “shuffle songs’’ command.⁴¹ We would like to give a confidence interval for the average audio file length μ for this iPod.

Table : TABLE 7.5 Length (in Seconds) of Audio Files Sampled from an iPod

240	316	259	46	871	411	1366
233	520	239	259	535	213	492
315	696	181	357	130	373	245
305	188	398	140	252	331	47
309	245	69	293	160	245	184
326	612	474	171	498	484	271
207	169	171	180	269	297	266
1847

471

FIGURE 7.20 Normal quantile plot of audio file length, Example 7.25. This sort of pattern occurs when a distribution is skewed to the right.

FIGURE 7.21 Normal quantile plot of the logarithms of the audio file lengths, Example 7.25. This distribution appears approximately Normal.

A Normal quantile plot of the audio data from Table 7.5 (Figure 7.20) shows that the distribution is skewed to the right. Because there are no extreme outliers, the sample mean of the 50 observations will nonetheless have an approximately Normal sampling distribution. The t procedures could be used for approximate inference. For more exact inference, we will transform the data so that the distribution is more nearly Normal. Figure 7.21 is a Normal quantile plot of the natural logarithms of the time measurements. The transformed data are very close to Normal, so t procedures will give quite exact results.