U1D6 Z-Scores Jan15
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NORMAL DISTRIBUTION %
Another Normal Distribution
Z-Score Formula
How Many Standard Deviations From the Mean?
Use the Z-Score to find out.
Parameter vs. Statistic
In your class, 27% of all students say that history is their favorite subject. Is this a parameter or a statistic?
What is an example of confounding variable?
A confounding variable may distort or mask the effects of another variable on the disease in question.
For example, a hypothesis that coffee drinkers have more heart disease than non-coffee drinkers may be influenced by another factor.
What confounding variable could influence results?
You want to study whether a low-carb diet can cause weight loss. What confounding variable could influence results? How can you adjust the study to prevent the influence?
Margin of Error and Confidence Intervals
A confidence interval is the mean of your estimate plus and minus the margin of error. This is the range of values you expect your estimate to fall between if you redo your test, within a certain level of confidence. Confidence, in statistics, is another way to describe probability.
Confidence intervals are most often constructed using confidence levels of 95% or 99%.
Calculating Confidence Intervals
Suppose a group of researchers is studying the heights of high school basketball players. The researchers take a random sample from the population and establish a mean height of 74 inches.
The mean of 74 inches is a point estimate of the population mean. A point estimate by itself is of limited usefulness because it does not reveal the uncertainty associated with the estimate; you do not have a good sense of how far away this 74-inch sample mean might be from the population mean.
At a 95% confidence level, researchers calculate a margin of error of ±2, plus and minus 2.
Add and subtract 2 from the sample mean, 74, to get the confidence interval: (72, 76)
We are 95% confident the true mean of all high school basketball player heights is between 72 and 76 inches.
An automotive engineer wants to estimate the cost of repairing a car that experiences a 25 MPH head-on collision. He crashes 24 cars, and the average repair is $11,000 with a margin of error of ±$1,500.
Calculate the confidence interval for the true mean cost of repairing a car that experiences a 25 MPH head-on collision.
A sample of 300 hundred eggs were randomly chosen from a female salmon and individually weighed. The mean weight was 0.978 grams with a margin of error of ± 0.005 grams.
Calculate the confidence interval for the true weight of salmon eggs.
Which of the following dot plots would most likely have the highest standard deviation?
Two different cable company’s basic channel line up and number of customers are nearly identical but the companies vary in their pricing based on location.
Carter Cable charges customers a mean monthly price of $60 with a standard deviation of $14
Eighty & Tee cable charges customers a mean monthly price of $60 with a standard deviation of $5
Which of the following statement is most likely to be true?
Use the Box-and-Whisker Plot to identify the third quartile, Q3.
Consider the following Basic Box & Whisker Plot.
What is the Interquartile Range (IQR) of the data set shown in the graph?
Which is the best definition of an Outlier?
Consider the following Ordered Data Set. 2, 3, 5, 7, 7, 9, 10 Which is a correct box and whisker plot of the data above?
Find the area between the z-scores, z = 0 and z = 2.
The D.O.T. collected data for a particular stretch of I-85 and found that the average speed was 70 mph with a standard deviation of 15 mph and the distribution is approximately normally distributed. The actual Speed Limit for the stretch of road is a maximum of 70 mph and minimum of 40 mph. What percentage of drivers actually drive between 40mph and 70 mph?
