The student will demonstrate and compare properties of the central limit theorem.
Note
This lab works best when sampling from several classes and combining data.
Collect the data
Count the change in your pocket. (Do not include bills.)
Randomly survey 30 classmates. Record the values of the change in
[link] .
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Construct a histogram. Make five to six intervals. Sketch the graph using a ruler and pencil. Scale the axes.
Calculate the following (
n = 1; surveying one person at a time):
= _______
s = _______
Draw a smooth curve through the tops of the bars of the histogram. Use one to two complete sentences to describe the general shape of the curve.
Collecting averages of pairs
Repeat steps one through five of the section
Collect the Data. with one exception. Instead of recording the change of 30 classmates, record the average change of 30 pairs.
Randomly survey 30
pairs of classmates.
Record the values of the average of their change in
[link] .
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Construct a histogram. Scale the axes using the same scaling you used for the section titled
Collect the Data . Sketch the graph using a ruler and a pencil.
Calculate the following (
n = 2; surveying two people at a time):
= _______
s = _______
Draw a smooth curve through tops of the bars of the histogram. Use one to two complete sentences to describe the general shape of the curve.
Collecting averages of groups of five
Repeat steps one through five (of the section titled
Collect the Data ) with one exception. Instead of recording the change of 30 classmates, record the average change of 30 groups of five.
Randomly survey 30
groups of five classmates.
Record the values of the average of their change.
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Construct a histogram. Scale the axes using the same scaling you used for the section titled
Collect the Data . Sketch the graph using a ruler and a pencil.
Calculate the following (
n = 5; surveying five people at a time):
= _______
s = _______
Draw a smooth curve through tops of the bars of the histogram. Use one to two complete sentences to describe the general shape of the curve.
Discussion questions
Why did the shape of the distribution of the data change, as
n changed? Use one to two complete sentences to explain what happened.
In the section titled
Collect the Data , what was the approximate distribution of the data?
X ~ _____(_____,_____)
Step 1: Find the mean. To find the mean, add up all the scores, then divide them by the number of scores. ...
Step 2: Find each score's deviation from the mean. ...
Step 3: Square each deviation from the mean. ...
Step 4: Find the sum of squares. ...
Step 5: Divide the sum of squares by n – 1 or N.
The sample of 16 students is taken. The average age in the sample was 22 years with astandard deviation of 6 years. Construct a 95% confidence interval for the age of the population.
Bhartdarshan' is an internet-based travel agency wherein customer can see videos of the cities they plant to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400
a. what is the probability of getting more than 12,000 hits?
b. what is the probability of getting fewer than 9,000 hits?
Bhartdarshan'is an internet-based travel agency wherein customer can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400.
a. What is the probability of getting more than 12,000 hits