Answers: Inference

Homework 5: Inference

Answers to odd number problems

1.                Ho in population
            True     False
         --------------------
                   |
reject Ho    FP    |   TP
                   |
          --------------------
                   |
accept Ho    TN    |.  FN
                   |

so we have:
* FP goes with Type I error
* FN goes with Type II error

3. test statistic is value of test (e.g., t-test, chi-square) calculated from results. Critical value is value from the appropriate distribution associated with a known probability.

5. lots of possible answers

7. Two tailed. No reason to specify a particular hypothesis, like, more red than green. Null hypothesis: candy colors in equal proportions; alternate hypothesis: candy colors not in equal proportions

9. Implies a two tailed test: Null hypothesis: Effectiveness of old and new drugs are the same; Alternate hypothesis: Effectiveness of old and new drugs are not the same.

Regarding side-effects, secondary hypotheses one tailed: Null hypothesis: new drug has the same or more side effects; Alternate hypothesis: new drug has fewer side effects

11. Calculate the standard error of the mean: 0.4110961, 0.2373464, 0.8221922, 0.4746929

approx lower, approx upper limits
    12.17781,     13.82219
    12.52531,     13.47469
    11.35562,     14.64438
    12.05061,     13.94939

11b. width of confidence interval proportional to size of variability; greater the variability the wider the interval, and therefore the less certain we are about our estimate.

11c.Width of confidence interval inversely proportional to sample size; greater the sample size the narrower the interval, and therefore the more certain we are about our estimate.

For 11, I used R as a calculator. Here’s some of my code

mySEM <- c(1.3/sqrt(10), 1.3/sqrt(30), 2.6/sqrt(10), 2.6/sqrt(30))

upper <- 13+2*mySEM
lower <- 13-2*mySEM

myDiff <- upper - lower

sort(mySEM)
sort(myDiff)