Download More Unit 7 Review - Spokane Public Schools

More Unit 7 Review
Name _______________________
Period ________ Date _________
1. On a New York – to – Denver flight, 8% of the 125 passengers were selected for random
security screening before boarding. According to the TSA, 10% of passengers at this airport
are chosen for random screening.
Which numbers represent the statistic and which number represents the parameter? What
are the units each number is measuring?
2. Does the following graphs represent a sample that is an unbiased estimator of the
population? Explain.
3. The histogram below left shows the intervals (in minutes) between eruptions of the Old
Faithful geyser for all 222 recorded eruptions during a particular month. For this population,
the median is 75 minutes. The histogram below right was created using software to take a
look at 500 SRSs of size 10 from the population, and displaying each of the 500 sample
medians. It was found that the mean of the sample medians is 73.5 minutes.
a) Is the sample median an unbiased
estimator of the population median? Explain.
b) Suppose we have taken samples of size 20 instead of size 10. Would the spread of the
sampling distribution be larger, smaller, or about the same? Explain.
c) Describe the shape of the sampling distribution. Explain what this means in terms of
overestimating or underestimating the population median.
4. About 75% of young adult Internet users (ages 18 – 29) watch online video. Suppose that
a sample survey contacts a SRS of 1000 young adult Internet users and calculates the
proportion p̂ in this sample who watch online video.
a. What is the mean of the sampling distribution of p̂? Explain.
b. Find the standard deviation of the sampling distribution of p̂. Check that the 10%
condition is met.
c. Is the sampling distribution of p̂ approximately normal? Check that the normal
condition is met.
d. If the sample size was 9000 instead of 1000, how would this change the sampling
distribution of p̂?
5. A polling organization asks a SRS of 1500 first-year college students how far away their
home is. Suppose that 35% of all first-year students actually attend college within 50 miles of
home. What is the probability that the random sample of 1500 students will give a result
within 2 percentage points of this true value? (use a modified p̂ version of your z-score
equation)
6. The height of young women follows a Normal distribution with µ = 64.5 inches and σ = 2.5
inches.
a. Find the probability that a randomly selected young woman is taller than 66.5 inches.
b. Find the probability that the mean height of a SRS of 10 young women exceeds 66.5
inches.
c. What is the difference in a and b above?
7. Everyone wants to have the latest technological gadgets and battery manufacturers are
constantly searching for ways to build longer-lasting batteries. One particular manufacturer
produces AA batteries that are designed to last an average of 17 hours with a standard
deviation of 0.8 hours. Quality control inspectors select a SRS of 30 batteries during each
hour of production to test their lifetimes (in hours).
a.
Since we don’t know what the population distribution looks like, check that all
conditions are met so that we can utilize the central limit theorem in respect to the
sampling distribution.
b. What is the probability of getting a SRS of size n = 30 with a sample mean of 16.7 hours
or less?