Can I please get help on the "Sample Mean or Sample Proportion" problem?
Transcribed Image Text:Sample Mean or Sample Proportion?
For each of the following data sets, explain whether we would be interested in the sample mean or the
sample proportion, and why. (Hint: Is the data quantitative or categorical?)
N
D
The lung capacities, in cubic centimeters, of 100 adults.
A survey of 50 people asking whether they prefer red or blue.
How many of the 25 students in a class scored above 70% on a given assignment.
The widths, in nanometers, of 80 amino acid chains.
Recall from Week 6 that the criteria for assuming "almost" independence, when determining whether a
binomial distribution is appropriate for a random variable with two possible outcomes, is that the
population size is more than ten times larger than the sample size. Assuming we have this condition met,
why do we then care about the criteria np > 10 and n (1-p) > 10? (Relate this to another concept we
explored in Week 6.)
Back in Quality Control!
For this portion, refer to the Week 6 Collaborative SMP Assignment, the scenario with the quality control
testing:
Why can we not use the z scores associated to the probabilities in these sampling distributions to
answer these questions? Be specific.
Change the numbers in the scenario, to resolve the issue you just explained, and explain why these
changes resolve the issue.
Sketch the sampling distributions resulting from your changed numbers and rephrase the questions in
terms of sampling distributions.
Answer the questions in the scenario, with your new numbers, using the tools from this week for the
sampling distribution of a sample proportion.
MUTITIMA
31
US
Nov 1
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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