Q 8.91. - Elementary Statistics

Question

LEDs and CFLs. Light-emitting diodes (LEDs) and compact fluorescent lights (CFLs) are lightbulbs that are supposed to last up to fifty times longer than old-fashioned incandescent lightbulbs and also use less energy. Consumer Reports sampled eighteen different $60-$watt LED and CFL lightbulbs. The following table lists their brightness. in lumens. Use the technology of your choice to decide whether applying the $z-$interval procedure to these data is reasonable. Explain your answer.

Step-by-Step Solution

Answer

It can be concluded that the applying $z-$interval procedure to the given data is not reasonable.

Step 1: Given information

900	690	910	745	765	820
700	360	925	805	850	730
865	680	750	735	865	635

Step 2: Explanation

Check whether using the $z-$interval technique on the given data is appropriate.

Draw the normal probability plot for Brightness with MINITAB.

Procedure for MINITAB:

Step 1: Select Probability Plot from the Graph menu.

Step 2: Click OK after selecting Single.

Step 3: In the Graph variables section, add the Brightness column.

Step 4: Click the OK button.

MINITAB OUTPUT

Draw the Brightness histogram with MINITAB.

Procedure for MINITAB:

Step 1: Select Histogram from the Graph menu.

Step 2: Click OK after selecting Simple.

Step 3: In the Graph variables section, type in the Brightness column.

Step 4: Click the OK button.

OUTPUT FROM MINITAB: 

Step 3: Explanation

The distribution of the variable is not normally distrusted, as the points are not closer to the straight line, as shown by the normal probability plot.

The distribution of the variable is not generally distrusted, according to the normal histogram, because the form of the distribution is skewed to the left with an outlier. Furthermore, the sample size is limited. As a result, it can be inferred that using the $z-$interval technique on the given data is not appropriate.