when appropriate and complete sentences which explain all analysis that was done in addition
to all conclusions and results. All work should be your own. Plagiarism will result in a project
score of 0.
You will be performing an analysis on female heights, given of set of 30 heights that were
randomly obtained. For this project, it is necessary to know that the average height for women
is assumed to be 65 inches with a standard deviation of 3.5 inches. You will use these numbers
in some of your calculations.
Steps:
1. Download the data . This is the data that you will use throughout this
project.
2. Find Elizabeth in the data and, given the population mean and standard deviation,
calculate:
a. The z-score for Elizabeth (easiest to be done by hand).
b. The probability that a randomly selected female is shorter than Elizabeth.
c. The probability that a randomly selected female is taller than Elizabeth.
d. Interpret each of these in a sentence (3 full sentences).
e. HINT: for this step you should use the mean and standard deviation that are
given in the paragraph above “Steps”. You should not use a sample mean or
sample standard deviation calculated from the data given.
3. As you know, a random sample of 30 women’s heights was obtained. Describe the
sampling distribution. Use a full sentence here to describe the sampling distribution.
HINT: See the Chapter 8 Lecture Notes Key or the Chapter 8 video lecture if you are
stuck. You will not use the raw data yet.
4. In StatCrunch or Excel, find and state the mean of the 30 women’s heights that were
provided (round to two decimal places). Then (using the values from step 3), calculate
the probability that a random sample of 30 women’s heights would result in a mean
that was the value you found or more. Use this probability in a full sentence.
5. Explain how what you just calculated in step 4 relates to the question you were asked in
step 2c. Why is the probability in step 4 lower than that in step 2?
6. For this step, please work under the assumption that we do not know the population
mean and standard deviation (and in fact, if we are running this test, it means that we
are not sure of these values). Construct a 95% confidence interval for the average height
of a female. Interpret this confidence interval. HINT: You can use the “with data” option
in StatCrunch to do this calculation.
Math 200 – Project 2
7. It is a researcher’s belief that the average height of females has increased since the
average value of 65 inches was reported. Using the sample of 30 female heights,
conduct a hypothesis test at the .05 level that tests whether or not this researcher might
be correct. You must state the null and alternative hypotheses as well as the p-value and
an interpretation of what this means. HINT: You can use the “with data” option in
StatCrunch to do this calculation.
8. How do the results from steps 6 and 7 relate to one another? HINT: does the true mean
(given above these steps) lie in the interval found in step 6? How is this confirmed by
the result in step 7?
9. Put everything together into an organized paper and submit it