1. [25 pts] Confidence Interval
In study of maximal aerobic capacity, 14 women had their blood plasma volume measured The
following data their blood plasma volumes measured liters.
3.59
2.66
2.81
3.12
2.65
3.85
3.05
2.98
3.87
3.28
2.95
3.51
1.12
3.22
Assume that women blood plasma volume normally distributed random variable
a.
Calculate point estimate of the population meang of women's blood plasma volume
b.
Calculate the sample standard deviation (you canuse 1-var stats on your calculator of the women's
blood plasma volume
c. We want to finda 95% con fidence interval. What the critical value Ca/2? Please show your work
d. Construct 95% confidence interval for the mean women's blood plasma volume by using the
formula. Indicate clearly what the value of the point estimate and the margin of error. Show your
work.
e
Interpret the confidence interval that you constructed
2.
[25 pts] Confidence Interval
A survey was conducted in which 764 randomly selected Americans were asked if they always use
seatbelts when in motor vel icle. and 635 of them responded that they do use seatbelts
a. Calculate point estimate of the population proportion pof Americans who use seatbelts.
b. We want to find 92% con fidence interval Thisi not typical confidence level, so you need to
calculate the critical value Z/2- Please show your work.
c. Construct 92% confidence interval for the proportion of Americans who use seatbelts when in a
motor vehicle by using the formula. Indicate clearly what the value of the point estimate and the
margin of error. Show your work.
d. Write a sentence to interpret the confidence interva that you constructed.
e.
The results of this survey are few years olo and the polling organization plans to redo the survey so
they canget more up-to date information. They would still like to use 92% confidence level and
they want to have margir of error that no morethan 2% What sample size should they use for
their new urvey? Round up to the nearest wholenumber.
3.
[25 pts] Hypothesis Test
The College Boar reported that the mean tuition and fees at community colleges nationwide for the
2013 2014 academic year was $3264. In order to determine whether costs have increased since then a
random sample of 16 community colleges was obtained. The sample mean tuition and fees was $3540
with sample standard deviation of $439 Test whether community college tuition and fees have
increasedusing levelof significance a=.05.
a. State the null and alternative hypotheses.
b. Calculate the test statistic Show your work.
c. Below standard normal -distribution curve (whichever appropriate forthis problem).
Mark your test statistic on the curve, shade the correct area, and indicate clearly whatonthe curve
represents the
d.
Calculate the p-value. Show your work or what you put inthe calculator. (Remember you are not
allowed to use anything in the STAT TESTS menu, but you canuse functions in the 2nd VARS menu)
e. Are you going to reject o fail to reject the null hypothesis? How did you decide?
f. State your conclusion (without using word: like "reject" and "hypothesis'
4. [25 pts]Hypothesis Test
The National Academy of Science reported ir 1997 that 40% of researchin mathematics is published by
U.S. authors. The mathematics chairperson of : prestigious university wonders whether this percentage
has thanged he has no indication of whether the percentage may have increased or decreased since
that time He surveys simple random sample of 131 recent articles published by reputable
mathematics research journals and findsthat 61 of the articles have U.S authors.
Perform your hypothesis test at the a=.10 level of significance.
State the null and alternative hypotheses
b. Calculate the test statistic. Show your work.
c.
Below standar normal t-distribution curve (whicheveri appropriate forthis problem)
Mark your test statistic on the curve, shadet the correct area, and indicate clearly what onthe
curve represents the P-Value^
d. Calculate the P-value. Show your work or what you put inthe calculator. (Remember you are not
allowed to use anything the STAT >> TESTS menu, but you can use functions in the 2nd VARS menu)
Are you going to reject or fail to reject the null hypothesis? How did you decide?
f. State your conclusion (without using words like "reject" and "hypothesis")
5. OPTIONAL EXTRA CREDIT: (up to +20 points)
Re-do both hypothesis tests fully demonstrating the critical value method
Make sure that you:
.
Write down the hypotheses and the test statistic.
Determine the critical value(s) and explain how you determined what the critical valueis.
.
Draw: picture of the normal/t-distribution curve, clearly indicating the critical value(s) and the critical
region.
Clearly mark the test statistic on your picture
.
Will you reject or fail to reject the null hypothesis? Explain your decision.
.
State the conclusion.
Do NOT calculate or use the p-value at any point during the process.

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1.
a) Calculate a point estimate of the population mean μ of women’s blood plasma volume.

Point Estimate of Mean µ = 3.190
I used 1-Var Stats function and calculated mean of all numbers....

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