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ANTONII [103]
3 years ago
12

An equal number of students from two Algebra 1 classes at Bozeman School were randomly selected and asked how many hours per wee

k they spend studying algebra.
The class with the largest median for hours spent studying is
-Mrs. Castro’s class
-Mr. Philippe’s class
-The medians are the same

The class with the largest range of hours spent studying is
-Mrs. Castro’s class
-Mr. Philippe’s class
-The ranges are the same

The class with the largest IQR for hours spent studying is
-Mrs. Castro’s class
-Mr. Philippe’s class
-The IQRs are the same

Mathematics
1 answer:
cricket20 [7]3 years ago
6 0

Answer:

Largest Median: Same

Largest Range: Castro

Largest IQR: Castro

Step-by-step explanation:

With a box-and-whisker plot, the box represents the upper and lower quartiles, the vertical line inside the box represents the median, and the lines on either side of the box show the high and low of the range.

Largest Median: Medians are the same because the verticle line inside the boxes is at 7 for both

Largest Range: Ms Castro's Class- the lines on either side of the box for Ms Castro go from 1-10 while the other class only goes from 4-10.

Largest IQR (interquartile range) Ms. Castro's class: their IQR goes from 5-8 while the other class only goes from 6-8

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We have a sample of 28 data points. The sample mean is 30.0 and the sample standard deviation is 2.40. The confidence level required is 98%. Then, we calculate α by:

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The confidence interval for the population mean, given the sample mean μ and the sample standard deviation σ, can be calculated as:

CI(\mu)=\lbrack x-Z_{1-\frac{\alpha}{2}}\cdot\frac{\sigma}{\sqrt[]{n}},x+Z_{1-\frac{\alpha}{2}}\cdot\frac{\sigma}{\sqrt[]{n}}\rbrack

Where n is the sample size, and Z is the z-score for 1 - α/2. Using the known values:

CI(\mu)=\lbrack30.0-Z_{0.99}\cdot\frac{2.40}{\sqrt[]{28}},30.0+Z_{0.99}\cdot\frac{2.40}{\sqrt[]{28}}\rbrack

Where (from tables):

Z_{0.99}=2.33

Finally, the interval at 98% confidence level is:

CI(\mu)=\lbrack28.94,31.06\rbrack

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