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Step-by-step explanation:
8. As the name implies, a box-and-whisker plot looks like a box with two whiskers. The box is the middle 50%. The whiskers are the bottom 25% and the top 25%.
First, we need to sort the numbers from smallest to largest. Starting with Set A:
Set A = {56, 57, 62, 68, 71, 82, 84, 92, 97, 101, 103, 106}
Now we find the median of the set, or the middle number. Set A has 12 data points. Since 12 is an even number, the median will be the average of the 6th and 7th numbers.
M = (82 + 84) / 2 = 83
Next, we find the median of the lower half. There are 6 numbers in the lower half, so the median is the average of the 3rd and 4th numbers.
Ml = (62 + 68) / 2 = 65
Now we find the median of the upper half. Again, there are 6 numbers in the upper half, so the median will be the average of the 3rd and 4th numbers.
Mu = (97 + 101) / 2 = 99
So the left whisker is from 56 to 65.
The box is from 65 to 99.
The right whisker is from 99 to 106.
Don't forget to mark the median, 83.
Repeat for Set B.
Set B = {36, 37, 42, 46, 48, 56, 58, 63, 69, 72, 75, 78}
M = (56 + 58) / 2 = 57
Ml = (42 + 46) / 2 = 44
Mu = (69 + 72) / 2 = 70.5
So the left whisker is from 36 to 44.
The box is from 44 to 70.5.
The right whisker is from 70.5 to 78.
The median is 57.
By graphing both on the same number line, we can easily compare them.
9. To make a dot plot, draw a number line starting from the smallest number and ending at the largest number. For each number, draw a dot every time the number appears in the set. For example, the number 3 appears twice in Set A, so draw two dots on 3. You may find it helpful to sort the data first.
10. Draw a dot plot of the set to determine the shape.
Answer:
The 95% confidence interval for the difference in the proportion of cancer diagnoses between the two groups is (0.3834, 0.5166).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction between normal variables.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
The randomly sampled 400 dogs from homes where an herbicide was used on a regular basis, diagnosing lymphoma in 230 of them.
This means that:
Of 200 dogs randomly sampled from homes where no herbicides were used, only 25 were found to have lymphoma.
This means that:
Distribution of the difference:
Confidence interval:
The confidence interval is:
In which
z is the zscore that has a pvalue of .
95% confidence level
So , z is the value of Z that has a pvalue of
, so
.
The lower bound is
The upper bound is
The 95% confidence interval for the difference in the proportion of cancer diagnoses between the two groups is (0.3834, 0.5166).