Name: ______
Make Up Test
Math 5 – Spring 2007
Due: Friday, May 17, by 11:40pm
No late exams will be accepted!!
Instructions:Show all work to support your answers for the following. For any hypothesis test the null and alternative hypotheses, the test statistic must be shown and the conclusion must be stated in terms of the original research hypothesis. For confidence intervals the calculation of E must be shown and the interval given as a compound inequality. For descriptive statistics all work must be supported with formulas, but you may use your calculator to get the numbers used in the formulas.
1. Spacelab Life Sciences 2 contained 14 male rats. After their return from space
their red blood cell mass (in mL) was determined. The same was done for a
control group of 14 male rats that never left the lab on Earth. The data is listed below.
Space: 8.59, 8.64, 7.43, 7.21, 6.87, 7.89, 9.79, 6.85, 7, 8.8, 9.3, 8.03, 6.39, 7.54
Lab: 8.65, 6.99, 8.4, 9.66, 7.62, 7.44, 8.55, 8.7, 7.33, 8.58, 9.88, 9.94, 7.14, 9.14
(Data taken from: Statistics: Informed Decisions Using Data, ed. 2, Michael Sullivan, III)
a)For the Space data compute the mean and standard deviation. (Be sure to double
check it against a calculator or computer, but show the work as asked in the instructions.)
b)For the Lab data compute the mean and standard deviation. (Be sure to double
check it against a calculator or computer, but show the work as asked in the instructions.)
c)For Lab data, create a frequency table with a class width of 0.6(there should be
5 classes). Make the lowest lower class limit 6.95.
d)Draw a histogram for Lab data based upon the frequency table in c).
e)Find the median, Q1 and Q3 and the minimum and maximum values of the Space
group. You must show work for the indicator values used in finding the quartiles.
f)Draw a boxplot for the Space Group. It must be drawn to scale.
g)Comment on the probable normality of the Space and Lab Groups, referring to
parts d) & f).
h)Now, let’s assume that the population from which the data was taken can be
assumed to be normally distributed. Using the data from Space group, find a 95%
confidence interval for the mean.
i)Still making the assumption of normality, find a 90% confidence interval for the
standard deviation of the population using the Lab data.
j)Using the Lab data, test the hypothesis that the mean of the population isn’t
8.5 at the = 0.05 level.
k)It is revealed, for this one part, that = 1. Using the Space data, test the
hypothesis that the mean of the population is smaller than 8.5 at the = 0.1 level.
l)Using the Space data, test the hypothesis that the standard deviation is actually more that 1. Use an = 0.01
m)Test the hypothesis that the groups come from different populations with different
populations means. Use = 0.1. Continue to assume normality, but is unknown.
2.The following information was found in two separate surveys taken on the publics’ support of the President.
Gallup Poll 5/15/06Wall Street Journal 5/13/06
Showed a 31% approval rateShowed a 29% approval rate
When 1,013 were surveyedWhen 1,003 were surveyed
a)Find a 95% confidence interval for the proportion of the population that approves of the President according to the Gallup Poll.
b)Using the data from the Wall Street Journal survey, at an = 0.1 level, test the claim that the President’s approval rating is better than that of Truman’s approval rating of 23% (an historically low approval rating).
c)At an = 0.05 level, test the claim that there not a difference between the Gallup Poll and the Wall Street Journal Poll.
3.The following is paired data. The first row is averages of exams for one of my past Statistics classes. The second row is the score on the final for the person with the given average on exams. See if there is a correlation in the data. I’ll walk you through the process by asking you questions. Just answer the following.
88, 90, 77, 88, 82, 63, 76, 103, 99, 84, 55, 93, 84, 59, 82, 69, 95, 90, 74, 85, 98, 77
76, 53, 82, 78, 70, 58, 47, 85, 81, 64, 1, 78, 79,63, 76, 75, 91, 75, 54,88, 77, 62
a)Draw a scatterplot of the data. Use the exam scores as independents and the final scores as dependents.
b)Does there appear to be correlation?
c)Find the mathematical value of the correlation.
d)Test the hypothesis that there is correlation at = 0.1. Use a t-statistic
e)Form the equation of the regression line that describes the relationship between exam scores and final scores.
f)Compute your average test score for this class.
g)You are a member of the population of students that have taken my Statistics class. Use the regression line to predict your grade on the final!
4.Assume that the following table the letters A, B, C, & D represent the choices on
the first question of a multiple choice quiz. The first row represents the choices of
men and the second row represents choices of women. The data represents
frequency counts in a randomly chosen sample of a population that was given a
certain multiple choice quiz and there were 66 men who answered A on the first
quiz question and 77 women who answered A, and so on.
A / B / C / DMen / 66 / 80 / 82 / 75
Women / 77 / 89 / 94 / 84
a)What is the probability that a randomly chosen response would be C based
upon this sample? (Give as a fraction and a decimal rounded to 3 places)
b)Under classic probability what would be the probability that a response
would be C? (Give as a fraction)
c)If we use the table to determine the probability that a response was made
by a man and the response was C, what do we find the probability to be? (Give as a fraction and a decimal rounded to 3 places)
d)If we say that these two things (response from a man and a response of C) are
independent events, what is the probability of the response being made
by a man and the response being a C? (Give as a fraction and a decimal rounded
to 3 places)
These questions from here are EC:
e)Test the claim at the = 0.01 level, that men and women choose different
answers in the same proportions. (State H0,HA, Show how to calculate Test Stat &
give value, Calculate Expected Value for Men/C cell by hand, Critical Value, State
conclusion.)
f)How does question e) relate questions c) & d)?
g)Just looking at the men’s data, test the hypothesis at the = 0.01 level that
the responses were not guesses. (State H0,HA, Show how to calculate Test Stat &
give value, Calculate Expected Value for Men/C cell by hand, Critical Value, State
conclusion.)
h)How does question g) relate questions a) & b)?
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