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Suggested Questions for Homework or Projects

Activity 4: How many raisins are in 1/2 oz box?

Questions for Key Concepts:

 
1)Download a random sample of 60 cases from the raisin activity database and analyze the
  data to answer the following questions.
a) Compare the distributions of the actual counts and the guesses based on
  • the shape of the distribution.
  • the variation of the distribution.
  • the center of the distribution.

b) Obtain the numerical summaries including mean, median, standard deviation, 1st quartile, 3rd quartile and min and max for actual and counts and guesses. Then write a brief discussion to compare the characteristics of actual counts and guesses.

c) Determine your point estimate for estimating

  • population mean counts
  • population standard deviation

d) Explain why it is not good to use the sample guess averages and standard deviation to estimate the population properties.

e) When the sample average counts to estimate population average count using this sample, what is the standard error of mean?

f) Determine a 90% and a 99% confidence interval for estimating the population average count. Explain each interval and determine which one is wider. Is it true that the higher the confidence level the wider the interval based on the same sample?

g) Explain why we should not use standard deviation obtained from the sample to quantify the error of using sample mean for estimating population mean in the context of this raisin case.

 

2) Download a random sample of 15 cases from the raisin activity database.

a) Answer the same question as 1(a).

b) Answer the same question as 1(b).

c) Answer the same question as 1(c).

d) Compare the mean, median, standard deviation, min and max between the data set of 60 cases in (b) and the data set of 15 cases in 2 (b). Write a brief discussion of your observation.

e) Answer the same question as 1(e).

f) Answer the same question as 1(f).

g) Question 1 uses n=60 cases and question 2 uses n=15 cases. Compare the two 90% confidence intervals, what do you find? Which gives a wider interval? n=60 or n=15?

h) Based on the pattern you observed in (g), is it true in general that when sample size increases, the confidence interval becomes narrower using the same confidence level?

 

 

 

 

 
 

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