WEEK 5 – HOMEWORK 5:

THE REQUIRED WEEK 5 PROBLEM SET IS ON THE ATTACHED WORD.DOCX.

(FROM LANE) Let’s start with the terms “point estimate” and “confidence interval”. You survey 100 units in a 1000 unit apartment building about whether they want cable and 67 units say they do want cable. This of course is 67/100 = 67% of the sample (relative frequency, right?). You now say that “based on your sample (or call it a poll) 67% of the entire apartment building population want cable. The 67% is called a “point estimate”.

But, how sure are you of that single number? Let’s say the cable company must be assured that at least 70% of the units want cable. To satisfy them, you compute a “confidence interval” around your point estimate (we will get to the calculations later). How “confident” do you want to be about this interval? Is being 90% confident OK, or 95%, or 99% ? These are the typical significance levels that we used in earlier work. HERE IS THE PART YOU NEED TO REALLY GET A FEEL FOR: THE HIGHER THE CONFIDENCE LEVEL THE WIDER (NOT NARROWER) THE CONFIDENCE INTERVAL BECOMES.

For our survey the 90% confidence interval could be 67% plus or minus (+) 4%. The 95% CI could be 67% + 10% and the 99% CI could be 67% + 15%. The last CI means that we are 99% confident that the interval from 52% to 82% contains the true value (usually we are talking about the mean). Would this 99% CI satisfy the cable company enough for them to install cable to the apartments? Probably. (If they understood statistics, they might do better using the 90% CI. Do you see that the more confident we want to be the WIDER our confidence interval must be? Make sure you do.

MAKE SURE TO USE THE TABLES (z-TABLES AND t-TABLES) FOR RELEVANT PROBLEMS (NOT SOFTWARE). THESE TABLES ARE AVAILABLE IN THE COURSE RESOURCES. SOFTWARE CAN BE USED TO CHECK YOUR ANSWERS.

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