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STATISTICS 101 - Module 4b Written Homework
Diamonds. Suppose you are planning to purchase a diamond and are curious about how much money
you would need to spend. A random sample of 351 diamonds was taken and their size (in carats) were
recorded.1 These data can be found in the JMP data file Diamonds.JMP.
1. Use JMP to calculate the sample mean price of diamonds and the sample standard deviation of the
price of diamonds.
Sample Mean Price = $7450.01
Sample Standard Deviation = $7780.89
2. How closely does the shape of the distribution of the price of diamonds follow the normal model?
Explain briefly.
The normal model has a symmetric and unimodal shape with a quantile plot that is linear, this
distribution does not follow the normal model as it is not symmetric, skews to the right and has a
curved line on a quantile plot.
3. Check to see if the three conditions that are needed to make confidence intervals and do hypothesis
tests for this example (you only need to check the conditions)
S A random sample of diamonds was taken.
1 ondition ( ): 351 diamonds is less than 10% of the diamonds available to purchase.
arly hough the price distribution is not normal, the sample size is big enough to
create a sampling distribution that tends toward a normal distribution. Because the model is highly skewed the
sample needs to be greater than 50-100, and it is.
4. Focus specifically on the Nearly Normal condition. Suppose the sample size had been 40 diamonds
instead of 351. Considering your answer to question 2, is it likely that a sample size of 40 would be
large enough to give us a sampling distribution that is approximately normal? Explain.
because states that as n increases the sample mean has a sampling
distribution tending toward a normal distribution. So even if the population distribution is not normal,
the sampling distribution can be. Given that our model is very skewed, we would need about 50-100
diamonds in order to arrive at a nearly normal sampling distribution. 40 diamonds is not enough to
obtain an approximately normal distribution.
1 Diamond data obtained from AwesomeGems.com on July 28, 2005.
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STATISTICS 101 - Module 4b Written Homework
Diamonds. Suppose you are planning to purchase a diamond and are curious about how much money
you would need to spend. A random sample of 351 diamonds was taken and their size (in carats) were
recorded.1 These data can be found in the JMP data file Diamonds.JMP.
1. Use JMP to calculate the sample mean price of diamonds and the sample standard deviation of the
price of diamonds.
Sample Mean Price = $7450.01
Sample Standard Deviation = $7780.89
2. How closely does the shape of the distribution of the price of diamonds follow the normal model?
Explain briefly.
The normal model has a symmetric and unimodal shape with a quantile plot that is linear, this
distribution does not follow the normal model as it is not symmetric, skews to the right and has a
curved line on a quantile plot.
3. Check to see if the three conditions that are needed to make confidence intervals and do hypothesis
tests for this example (you only need to check the conditions)
S A random sample of diamonds was taken.
1 ondition ( ): 351 diamonds is less than 10% of the diamonds available to purchase.
arly hough the price distribution is not normal, the sample size is big enough to
create a sampling distribution that tends toward a normal distribution. Because the model is highly skewed the
sample needs to be greater than 50-100, and it is.
4. Focus specifically on the Nearly Normal condition. Suppose the sample size had been 40 diamonds
instead of 351. Considering your answer to question 2, is it likely that a sample size of 40 would be
large enough to give us a sampling distribution that is approximately normal? Explain.
because states that as n increases the sample mean has a sampling
distribution tending toward a normal distribution. So even if the population distribution is not normal,
the sampling distribution can be. Given that our model is very skewed, we would need about 50-100
diamonds in order to arrive at a nearly normal sampling distribution. 40 diamonds is not enough to
obtain an approximately normal distribution.
1 Diamond data obtained from AwesomeGems.com on July 28, 2005.
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