You need to explain your work STEP by step and include all the calculations, not just the
1. 50 people are selected randomly from a certain population and it is found that 12 people in the
sample are over 6 feet tall. What is the point estimate of the proportion of people in the
population who are over 6 feet tall?
2. Find the appropriate critical value for the following:
99% confidence level; n = 17; σ is unknown; population appears to be normally distributed.
a. t α/2 = 2.898
b. t α/2 = 2.921
c. z α/2 = 2.583
d. z α/2 = 2.567
3. Find the critical value χ 2R corresponding to a sample size of 19 and a confidence level of 99
4. To find the standard deviation of the diameter of wooden dowels, the manufacturer measures
19 randomly selected dowels and finds the standard deviation of the sample to be s = 0.16. Find
the 95% confidence interval for the population standard deviation σ.
a. 0.13 < σ < 0.22
b. 0.12 < σ < 0.24
c. 0.15 < σ < 0.21
d. 0.11 < σ < 0.25
5. You want to estimate for the population of waiting times at a fast-food restaurant’s drive-up
windows, and you want to be 95% confident that the sample standard deviation is within 20% of
. Find the minimum sample size needed. Is this sample size practical?
6. In the 1960s, data were collected on the weights of people to determine the safe passenger
capacity of aircraft. Using a random sample, the mean weight was found to be 166.3 lbs.
In recent decades, the mean weight of the population has increased considerably, so we need to
update our estimate of that mean.
Recently, a simple random sample of the weights of n = 40 people was collected and found to
have a mean of = 172.55 lb.
We do not know the standard deviation, but this is the dispersion of the weights in general so it
should be between 30-50 pounds for adults. Let's assume that is 35
Let's assume the average here around 75. Let's assume a margin of error of 3%, how big should
our sample be?
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