Item 14 A recent increase in sales of microchips has forced a computer company to buy a new processing machine to help keep up with demand. The builders of the new machine claim that it produces fewer defective microchips than the older machine. From a random sample of 90 microchips produced on the old machine, 5 were found to be defective. From a random sample of 83 microchips produced on the new machine, 3 were found to be defective. The quality control manager wants to construct a confidence interval to estimate the difference between the proportion of defective microchips from the older machine and the proportion of defective microchips from the new machine. Why is it not appropriate to calculate a two-sample z-interval for a difference in proportions? The microchips were not randomly assigned to a machine. A There is no guarantee that microchips are approximately normally distributed. B The normality of the sampling distribution of the difference in sample proportions cannot be established. C Both sample proportions are less than 0.10. D The sample sizes are not the same.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Item 14
A recent increase in sales of microchips has forced a computer company to buy a new processing machine to help keep up with demand. The builders of the new machine claim that it produces fewer defective microchips than the older machine. From a random sample of 90 microchips produced on the old machine, 5 were found to be defective. From a random sample of 83 microchips produced on the new machine, 3 were found to be defective. The quality control manager wants to construct a confidence
Why is it not appropriate to calculate a two-sample z-interval for a difference in proportions?
-
The microchips were not randomly assigned to a machine.
A -
There is no guarantee that microchips are approximately
normally distributed. B -
The normality of the sampling distribution of the difference in sample proportions cannot be established.
C -
Both sample proportions are less than 0.10.
D -
The sample sizes are not the same.
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