STAT 11 2008-

1. Confidence interval for a mean.

Mars Rover Two measures 64 daily high temperatures, and finds that the average of the 64 measurements is -42.5 degrees C.  Assume that the standard deviation of daily temperatures is exactly 16 degrees C, based on data from Mars Rover One.

a. In this problem, what are n, μ, x^-, σ, and s?

b. What is the standard error of the mean temperature?

c. Give a 95% confidence interval for μ.

d. Give an 82% confidence interval for μ.

2. Confidence interval for a proportion.

You randomly selected 100 of your latest homemade stink bombs, and very carefully tested them.  Unfortunately 80 of them failed. Let p be the "true" failure rate (for all stink bombs, not just the ones in the sample).

a. What is p^{^}?

b. What is the SE?

c. What is a 95% CI for the true failure rate?

d. If you felt like using Wilson's method for this problem, what would change?

3. Confidence interval for a difference of means.

You found that 30 randomly selected Sunoco stations had an average gas price of $ 3.10, with s = $ 0.05. 

Also, 40 randomly selected Lukoil stations had an average price of $3.12, with s = $ 0.08. 

Let D = (average of all Lukoil prices) minus (average of all Sunoco prices).

What is a 95% confidence interval for D? What can you conclude about the relative prices at Lukoil and Sunoco stations generally?

4. Interpreting a scatterplot.

a. Look at this scatterplot, and estimate...

The mean of the "x" variable;

The standard deviation of the "x" variable;

The mean of the "y" variable;

The standard deviation of the "y" variable;

The correlation coefficient (r) for the two variables.

b. Describe the relationship in words.

5. More on standard errors.

Science News reported that the average length of a junk-DNA sequence in Speciesus Inventedus is 128 bases, based on a sample of 100 measurements.

a. What is the SE for μ, the true average length?

b. Actually, Science News gave the SE:  They said it's 8. What is the standard deviation of the original sample?

6. One-way chi-square problem.

A poker-dealing machine is supposed to deal cards at random, as if from an infinite deck.

In a test, you counted 1600 cards, and observed the following:

                                Spades                 404

                                Hearts                   420

                                Diamonds            400

                                Clubs                     376

Could it be that the suits are equally likely?  Or are these discrepancies too much to be random?

7. Another one-way chi-square problem.

Same as before, but this time jokers are included, and you counted 1662 cards, with these results:

                                Spades                 404

                                Hearts                   420

                                Diamonds            400

                                Clubs                     356

                                Jokers                     82

a. If a deck contains 54 cards and two of them are jokers, what is the probability that any particular randomly-chosen card would be a joker?

b. How many jokers would you expect out of 1662 random cards?  How many of each suit?

c. Is it possible that the cards are really random?  Or are the discrepancies too large?