Prediction: The proportion of defective flashlights will be between 4.83 % and 10.83 %.
Practice makes perfect
a
The Bright Idea Lighting Company takes many samples of flashlights over the week to determine the proportion of those that are defective.
Proportion of Defective Flashlights in 100 Samples
0.02
0.06
0.07
0.08
0.09
0.04
0.06
0.07
0.09
0.10
0.05
0.06
0.08
0.09
0.10
0.05
0.06
0.08
0.09
0.10
0.05
0.06
0.08
0.09
0.10
0.05
0.06
0.08
0.09
0.10
0.05
0.06
0.08
0.09
0.10
0.05
0.07
0.08
0.09
0.10
0.05
0.07
0.08
0.09
0.10
0.05
0.07
0.08
0.09
0.10
0.05
0.07
0.08
0.09
0.10
0.05
0.07
0.08
0.09
0.10
0.05
0.07
0.08
0.09
0.11
0.05
0.07
0.08
0.09
0.11
0.06
0.07
0.08
0.09
0.11
0.06
0.07
0.08
0.09
0.11
0.06
0.07
0.08
0.09
0.11
0.06
0.07
0.08
0.09
0.12
0.06
0.07
0.08
0.09
0.12
0.06
0.07
0.08
0.09
0.13
checksum
7.83
The mean proportion of defective flashlights is the sum of the proportions divided by the total number of samples. We can see in the table that the sum of the data values is 7.83 and that there are 100 samples. Let's use these values to find the mean.
7.83/100 = 0.783 or 7.83 %
The mean proportion of defective flashlights is 7.83 %.
b
To find the upper and lower bounds of the sample-to-sample variability, we need to make sure that the given data values are sorted from least to greatest. Notice that our data has already been sorted and ordered by columns.
Proportion of Defective Flashlights in 100 Samples
0.02
0.06
0.07
0.08
0.09
0.04
0.06
0.07
0.09
0.10
0.05
0.06
0.08
0.09
0.10
0.05
0.06
0.08
0.09
0.10
0.05
0.06
0.08
0.09
0.10
0.05
0.06
0.08
0.09
0.10
0.05
0.06
0.08
0.09
0.10
0.05
0.07
0.08
0.09
0.10
0.05
0.07
0.08
0.09
0.10
0.05
0.07
0.08
0.09
0.10
0.05
0.07
0.08
0.09
0.10
0.05
0.07
0.08
0.09
0.10
0.05
0.07
0.08
0.09
0.11
0.05
0.07
0.08
0.09
0.11
0.06
0.07
0.08
0.09
0.11
0.06
0.07
0.08
0.09
0.11
0.06
0.07
0.08
0.09
0.11
0.06
0.07
0.08
0.09
0.12
0.06
0.07
0.08
0.09
0.12
0.06
0.07
0.08
0.09
0.13
checksum
7.83
The lower and upper 5 % bounds are the 5th and 95th percentiles of the data. Then, in a set of 100 values, the lower 5 % bound is the 5th value on the list, and the upper 95 % bound is the 95th value on the list. Let's highlight them.
Proportion of Defective Flashlights in 100 Samples
0.02
0.06
0.07
0.08
0.09
0.04
0.06
0.07
0.09
0.10
0.05
0.06
0.08
0.09
0.10
0.05
0.06
0.08
0.09
0.10
0.05 (5th value)
0.06
0.08
0.09
0.10
0.05
0.06
0.08
0.09
0.10
0.05
0.06
0.08
0.09
0.10
0.05
0.07
0.08
0.09
0.10
0.05
0.07
0.08
0.09
0.10
0.05
0.07
0.08
0.09
0.10
0.05
0.07
0.08
0.09
0.10
0.05
0.07
0.08
0.09
0.10
0.05
0.07
0.08
0.09
0.11
0.05
0.07
0.08
0.09
0.11
0.06
0.07
0.08
0.09
0.11 (95thvalue)
0.06
0.07
0.08
0.09
0.11
0.06
0.07
0.08
0.09
0.11
0.06
0.07
0.08
0.09
0.12
0.06
0.07
0.08
0.09
0.12
0.06
0.07
0.08
0.09
0.13
checksum
7.83
The lower bound is 0.05 and the upper bound is 0.11.
c
To predict the proportion of defective flashlights in the whole population, we should formulate the margin of error. Remember, the margin of error in a data set is the difference of the upper and lower bounds divided by 2. We will use the values we found in Part B for this.
Margin of Error: &= 0.11 - 0.05/2 [0.5em]
&= 0.03 or 3 %
Finally, we can write our prediction. The predicted proportion of defective flashlights is the sample mean plus or minus the margin of error.
7.83 % ± 3 %
We predicted that the proportion will be between 7.83 - 3= 4.83 % and 7.83 + 3= 10.83 %.
