Question

6. It's presidential primary season and canvassers are out talking to voters. In a city that's known to have 20% registered republicans, 5 canvassers each go to 50 randomly selected homes to ask about voting preferences. Amazingly, every home has someone willing to talk. Which of the following is the most plausible sequence of republican voters met by these canvassers?

a. 5%, 80%, 65%, 8%, 70%

b. they're all equally plausible

c. 15%, 25%, 22%, 28%, 20%

d. 20%, 20%, 20%, 20%, 20%

7.

The average birthweight of babies in Oregon is 3500 grams with a standard deviation of 500 grams. You collected 100 samples of 100 babies and calculated the mean weight of each of the samples. You then graph the means that you've calculated. What does your distribution of sample means look like?

a. it's pretty normal

b. it has no particular shape

c. it's skewed either left or right

8.

Still thinking about your distribution of the samples of baby weights, what would the standard deviation of your 100 sample means be?

a. more than 500 grams

b. not enough information to know

c, less than 500 grams

d. same as the population, 500 grams

Answer 1

6 -

b. they're all equally plausible

Because unregistered voters might prefer republicans or other parties and we don't know about them. Had the city had only registered voters, then we would have expected to see some pattern in voting preferences

7 -

a. it's pretty normal

Because of central limit theorem which states - As the sample size increases, the sample distribution approaches population distribution. Any sample size greater than 30 will have a distribution of shape quite similar to population distribution given that the sample is drawn at random

8 -

a. more than 500 grams

Sample standard deviation is always greater than population standard deviation that is the reason we use standard error for estimating population standard deviation and standard deviation's formula is

population's std / sqrt (n)

where n is the sample size

clearly as n approaches higher values the standard error of the sample reduces

Since the sample standard deviation depends upon the sample, it has greater variability. Thus the standard deviation of the sample is greater than that of the population.