Download Sampling Distributions

Sampling Distributions
No Data Set Needed
Part I – Statistics and Parameters
In each situation, explain whether the value given in bold print is a statistic or a
parameter:
1. A polling organization samples 1000 adults nationwide and finds that 72% of
those sampled favor tougher penalties for persons convicted of drunk driving.
2. In their year 2000 census, the United States Census Bureau found that the
median age of all American citizens was about 35 years.
3. For a sample of 20 men and 25 women, there is a 14 centimeter difference in
the mean heights of the men and women.
4. A writer wants to know how many typing mistakes there are in her
manuscript, so she hires a proofreader who tells her that in all books of the
same length as hers, the average is 15 errors.
Explain whether p̂ or p is the correct statistical notation for each proportion described:
5. The proportion that smokes in a randomly selected sample of n = 300 students
in the 11th and 12th grades.
6. The proportion that smokes among all students in the 11th or 12th grade in the
United States.
7. The proportion that is left-handed in a sample of n = 250 individuals.
Part II- Sampling Distribution of Sample Proportion:
A newspaper conducts a poll to determine the proportion of adults who favor a
certain candidate. They ask a random sample of 400 people whether or not they
favor that candidate (Assume no bias!). Suppose the true proportion of adults
who favor the candidate is 64%.
1
1. The newspaper records the sample proportion who favors the candidate. What
is the approximate sampling distribution of the sample proportion? (i.e., what
is the name of the distribution, and what are its mean and standard deviation?)
Hint: Look at the notes on “Sampling Distributions for Sample Proportion”
2. What is the probability that the newspaper would have recorded a sample
proportion greater than 68%?
3. What is the probability that less than 55% of the newspaper respondents
would support this candidate?
Part III- Sampling Distribution of Sample Mean:
1 (three parts). Vehicle speeds at a certain highway location are believed to have
approximately a normal distribution with mean =60 mph and standard deviation =6
mph.
a. Speeds for a randomly selected sample of n = 16 vehicles will be recorded. Determine
the values that fill in the blanks in the following sentence. For samples of n = 16 vehicles,
there is about a 68% chance that the mean vehicle speed will be between ___ and ___.
b. Speeds for a randomly selected sample of n = 36 vehicles will be recorded.
Determine the values that fill in the blanks in the following sentence. For samples of n =
36 vehicles, there is
about a 95% chance that the mean vehicle speed will be between ___ and ___.
c (three parts). Using the information in part b, find the following:
i. The standard error of the sample mean, X
SE( X ) =
ii. If the sample mean speed of these 36 cars was 58 mph, use the Standard
Normal Table to find P( X < 58).
iii. Write an interpretation for this outcome in part ii.
2