Frequency Distribution and Percentiles

capooth

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Joined
Feb 19, 2009
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I have been working on this for a while not but unfortunately I am not good at Stats. Here are the remaining problems I am struggling with:

1. Here is a frequency distribution for an exam. The instructor did not publish a mean score or raw data. What is the mean score on this test?

Class Interval Frequency
46 to 50 9
41 to 45 11
36 to 40 18
31 to 35 27
26 to 30 47
21 to 25 45
16 to 20 29
11 to 15 19
6 to 10 13
1 to 5 9
Total 227


2. Looking at the data, I decide that the number of bends to breaking of 4.25 is intriguing. I want to know what percentile paperclips are in that fail at 4.25 bends. Please give me this for all, for males, and for females.
I am also intrigued by paperclips that break at 1.5 bends. What percentage of paperclips breaks at or below 1.5 bends? Please give me this for all, for males, and for females.
What percentage of paperclips breaks at or above 1.5 bends but at or below 4.25 bends? Please give me this for all, for males, and for females.


All Male Female
Mean 2.713125 2.817105263 2.630263158
St Dev 1.53562017 1.5032189 1.49586534
N 400 240 160


All Male Female
Percentile, 4.25 bends
Percentile, 1.5 bends
Percent between 1.5 and 4.25 bends



3. Perform a z-test to tell me whether the differences in the means of bends between the males and the females is statistically significant, alpha = .05. Use as the standard deviation the population standard deviation. In the formula pictured below, use the means for females minus the mean for males, rather than using a sample mean and the population mean.


All Male Female
Mean 2 2 2
St Dev 2.713125 2.817105263 2.630263158
N 1.53562017 1.5032189 1.49586534

The standard error of the population:

The z-score:

The critical z (assume 2-tailed, .05):
 
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