Mini Tab Assignment 8
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School
University Of Connecticut *
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Course
1000Q
Subject
Mathematics
Date
Feb 20, 2024
Type
docx
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5
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Assignment 8
Please answer all questions using the appropriate version of the dataset as assigned by your TA. Each graph must be labeled with
a title, axis labels, and a footnote with your name and section number. 1.
A local university boasts that its School of Engineering attracts the top students from around the country. As proof of
this claim, they say that the average Math SAT score for their students is higher than the average Math SAT score of 610 at most
other Engineering schools. A random sample of n = 28 Engineering students is taken, and their Math SAT scores are recorded.
You will use a version of the datafile MATHSAT.
a.
What are the appropriate null and alternative hypotheses?
Ha: u > 610
Ho: u = 610
b.
Do a probability plot to look for normality. Report your findings here.
a.
What is the appropriate test of hypothesis to perform, a z-test or a t-test? Why?
The appropriate test is a T-test because the data is normal and the standard deviation is not given. a.
Perform the test of hypothesis and include a Boxplot and a Histogram.
What is the value of the test statistic? -1.14
What is the p-value of the test? 0.868
What is your decision using α = .01? Fail to reject the null hypothesis Are there any outliers? No outliers.
Is the data fairly symmetric? No, the data is not fairly symmetric. It is skewed positively left. Can this School brag that their students really are top-notch? Why or why not?
No, they can not brag because their SAT scores
are not greater than the national average.
f.
Estimate the average Math SAT score of this school’s engineering students using a 95%
confidence interval. Note: To construct the confidence interval, repeat the steps that you just used to
create the hypothesis test and then, under Options, set the alternative hypothesis to mean ≠
hypothesized mean. Interpret the confidence interval.
95% CL: (552.5,626.5)
2.
Calcium is the most abundant and one of the most important minerals in the body. It works with phosphorus to build
and maintain bones and teeth. According to the Food and Nutrition Board of the National Academy of Sciences, the
recommended daily allowance (RDA) of calcium for adults is 800 milligrams. You will use a version of the datafile CALCIUM.
The data is the daily calcium intake (in mg.) for a sample of people with poverty level incomes. The researchers believe that the
mean daily calcium intake for poverty level income people is below the recommended 800 mg. (poor people don't get enough
milk, etc.). Assume that, from previous studies, σ = 60 mgs.
a.
What is the appropriate null and alternative hypotheses? Ho: u = 800
Ha: u < 800
b.
What is the appropriate test of hypothesis, a z-test or a t-test? Why?
The appropriate test of the hypothesis is the z-test because we know the standard deviation. c.
Do a boxplot and a histogram as part of the hypothesis test. Are there any outliers? Is the data symmetric? There are
no outliers and the data is skewed a bit to the right.
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d.
What is the value of the test statistic? -4.26
What is the p-value of the test? 0
What is your decision, for α = .05? Reject the null hypothesis. What is your conclusion about the calcium level of poor people?
The conclusion is that poor people do intake less than the
recommended daily calcium (800mg). 3.
The TV shows “Pretty Little Liars” and “Breaking Bad” are listed among the top 20 TV series during the years 2012-
2013. A recent survey claimed that 45% of college students named “Pretty Little Liars” as their favorite of the two shows. Fans
of “Breaking Bad”
believed that percentage was inflated (that is, these fans believe that the proportion of college students who
would say “
Pretty Little Liars”
was their favorite show is actually less that 45%). They decided to take a survey of 100 college
students. Each student was asked the question: “Did you prefer ‘Pretty Little Liars’ over “Breaking Bad”
during the years 2012-
2013?” Each person could answer either Yes or No. You will use a version of the datafile TV1. a.
State the appropriate null and alternative hypotheses.
Ho: p= 0.45
Ha: u < 0.45
b.
Perform the test of hypothesis.
What is the test statistic? -1.81
At α = .05, what is your decision? 0.035 is less than 0.05
Why? Reject the null hypothesis Write a short statement summarizing your results. It is concluded that the null hypothesis is rejected, therefore there is
enough evidence Pretty Little Liars is the favorite show.