Thursday HW = More Conditions Practice!

Tonight please complete each of the two questions below (more conditions practice)--tomorrow in class we'll continue looking at sampling distributions, how they are created, and how we can apply the Normal model to a sampling distribution.

Thursday HW (answers below):

1.) Some business analysts estimate that the length of time people work at a job has a mean of 6.2 years and a standard deviation of 4.5 years. Researchers plan to survey a representative sample of 1,100 Americans to estimate the probability that an American works at a given job for 10 years or more. Name the appropriate sampling distribution and verify that the conditions for inference have been met.

2.) It's believed that 4% of children have a gene that may be linked to juvenile diabetes. Researchers test 732 newborns for the presence of this gene, and find that 20 of them do have the gene. The 732 newborns were randomly selected from a group of parents who volunteered to be part of the study. Name the appropriate sampling distribution and verify that the conditions for inference have been met.
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If you are having any trouble with the conditions, or you just want to strengthen your understanding/ability to check them....

• I would recommend reading the "Assumptions and Conditions" sections on pages 413 and 422 before you do your homework (this will give you more info about the conditions and why we check them)
• Record this information/these writing templates in your notebook!
• The randomization condition and the 10% condition are checked for both sampling distributions (means and proportions).

• Random Sample: our sample should be collected randomly, or treatments should be assigned at random
• If it's stated that the sample was collected randomly...
• "The sample of __(define sample in context)_____ was collected randomly." 
• If it's not stated that the sample was collected randomly...
• "We can assume our sample of ____(define sample in context)___ was collected randomly."
• OR....
• "We can assume our sample of ____(define sample in context)___ is a representative sample."
• 10% Condition: sample size must be less than 10% of population size
• "Our sample of ___(sample in context)___ is (likely) less than 10% of ___(population in context)____."
• Sampling Distribution For Means: Large Enough Sample Condition
• "Our sample of ___(define sample in context)____ is large enough."
• Sampling Distribution for Proportions: Success/Failure Condition
• No writing here, this is a math one--check that np>10 and n(1-p)>10
• Substitute the numbers--don't just write np>10 and n(1-p)>10!

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And here are the links to the sampling distribution applets we'll be exploring in class today/tomorrow:

Reese's Pieces: Sampling Distribution for Proportions Applet

Sampling Distribution for Means Applet

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Homework Answer Key:

1.) It is stated that the sample of 1,100 Americans is a representative sample (this is why we want a random sample, to be confident it represents the population); a sample of size 1,100 is large enough to proceed; 1,100 Americans is less than 10% of all Americans. A sampling distribution for means is appropriate.

2.) The 732 newborns were randomly selected; 732 newborns is less than 10% of all newborn babies; (732)(0.04) > 10 and (732)(1 - 0.04) > 10. A sampling distribution for proportions is appropriate.