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The Final Exam Review problems are here:

MAT2572FinalReviewSpring2018

The answers and partial solutions are here:

MAT2572FinalReviewSpring2018-answers

This is the 100% corrected version. Somehow the uncorrected version was the one posted to Piazza, and then Ned tried to fix it and only fixed one of the errors. Sorry about that!

The Final Exam will have only 9 problems: there is some repetition of material in these problems.

You will be provided with a table of critical values for $\chi^{2}$, since many of your calculators will not compute these for you.

You will be allowed to use one 8.5 by 11 inch sheet of paper containing FORMULAS ONLY, which you should start preparing while you work these problems. Below are my suggestions, but it is up to you to see what formulas you need to recall while working the problems. You sheet must be handed in along with the exam paper.

Suggestions:

Bayes’ Theorem, and/or (even better) the two formulas below:

$P(A\cap B) = P(A|B)P(B)$ and $P(A\cap B) = P(B|A)P(A)$

$P(A) = P(A\cap B) + P(A\cap B’)$

The formulas for the  mean and standard deviations of the special probability distributions.

The formula for a confidence interval for the population mean, if the population standard deviation is known. (It uses Z)

The formula for a confidence interval for a population proportion

The formula for a confidence interval for a population variance

You may also want to include the syntax for computing the special probabilities on your calculator, if you tend to forget. For example, computing a normal probability on the TI-84 has the syntax:

normalcdf(lowerbound, upperbound, mu, sigma)

ALL R assignments are absolutely due by midnight of Thursday 24 May, no exceptions!

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Finding a confidence interval using t-test in R:

Work problem 7.4.8: I copied the problem below.

I have typed up the data already:

7.4.8data

Just click-hold on the link and choose “open in Rstudio”

You will create a vector containing the data, and then do a t-test on that vecotr of data using the t.test function.  Copy and paste to Piazza as you did with the previous assignment, and then type the confidence interval itself at the top of your post. When you type in the confidence interval, round the numbers to the nearest whole number.

7.4.8. The following table lists the typical cost of repairing
the bumper of a moderately priced midsize car damaged
by a corner collision at 3 mph. Use these observations
to construct a 95% confidence interval for μ, the true
average repair cost for all such automobiles with similar
damage. The sample standard deviation for these data is
s =$369.02.
Make/Model
Repair
Cost Make/Model
Repair
Cost
Hyundai Sonata $1019 Honda Accord $1461
Nissan Altima $1090 Volkswagen Jetta $1525
Mitsubishi Galant $1109 Toyota Camry $1670
Saturn AURA $1235 Chevrolet Malibu $1685
Subaru Legacy $1275 Volkswagen Passat $1783
Pontiac G6 $1361 Nissan Maxima $1787
Mazda 6 $1437 Ford Fusion $1889
Volvo S40 $1446 Chrysler Sebring $2484
Source: www.iihs.org/ratings/bumpersbycategory.aspx?

Second assignment: writing up about your Datacamp course that you chose for the snow day make-up.

You will make a post to this OpenLab blog. To do this you must join OpenLab and join this course – you may already have done this. Choose this course once you log in to OpenLab, and then click on “Dashboard” on the right side of the page. This will take you to the Dashboard where you will find a link “Posts” on the left side: use it to “Add New”.

In your post, you should do the following:

First, give your name.

Give the title of your course and the link to it: you can copy the link from this post

Describe briefly why you chose it.

Give a brief (but not vague!) description of the topics that are covered in that course.

Choose one specific example of a thing you learned that you found interesting or useful. Here you will details, and also tell us why you chose it to write about.

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Instructions for using the various graphing calculators are linked in this post.

Here is how hypothesis testing works for the t-test on the mean:

We first state our null hypothesis and alternative hypothesis.

For this type of test, the null hypothesis always has an = sign in it:

$H_{0}: \mu = \mu_{0}$

The alternative can have any one of three forms, depending on what is important to distinguish. Either $H_{a}: \mu \neq \mu_{0}$

or $H_{a}: \mu < \mu_{0}$

or $H_{a}: \mu > \mu_{0}$

Where $\mu_{0}$ is a number (the hypothesized value of the population mean).

Using the t.test function in R, or the t-test on your calculator, the information we get includes p-values.

A p-value measures the strength of the evidence (the sample data) against the null hypothesis. Here is another source that explains more about p-values. The smaller p is, the more sure we are that we should reject the null hypothesis.

In practice, we choose a value of $\alpha$, called the level of significance of the test. It represents the probability of making a Type I error. (Usually that means we want $\alpha$ to be small, 5% or less.) Then we look at the p-value returned by R or by the calculator. If $p \le \alpha$ we will reject the null hypothesis: otherwise, we accept the null hypothesis or reserve judgement.

Here are problems to practice deciding what form of the alternative hypothesis to use: (we did some of them in class)

Math2501HypothesisTestingProblems

Here are problems to practice using the t-test and drawing conclusions from it: #4-5 and 8-11 especially

Practice problems

Here is information for the TI-83 and TI- 84 calculators. You want to follow the “one-sample” T test instructions.

Here is information for TI-89: You want “testing on a mean”

Here is information for the Casio fx-9750gii

Again, look for 1-sample t-test.

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MAT2572Test4ReviewSpring2018

Answers and hints or partial solutions are below the fold… up to #5 for now, to be updated this evening…

Continue reading →

Also don’t forget:

We have class – make-up for one snow day – on Thursday 17 May

Monday 21 May will be for review

# Take a random sample of size 50 from the binomial distribution that relates to the Zener card experiment:

binom_sample1 <- rbinom(50, 25, 0.2)

# Print the values in binom_sample1

binom_sample1

# Get a 95% confidence interval for that sample data

t.test(binom_sample1, mu = 5)

# take another sample and call it binom_sample2, and do the same

Here is a resource. It shows for TI-83, 84, 89

MAT2572HypothesisTestingVocabulary

MAT2572HypothesisTestingVocabulary

[An old post which I am reposting here.]

As a technical note, a 95% confidence interval does not mean that there is a 95% probability that the interval contains the true mean. The interval computed from a given sample either contains the true mean or it does not. Instead, the level of confidence is associated with the method of calculating the interval. The confidence coefficient is simply the proportion of samples of a given size that may be expected to contain the true mean. That is, for a 95% confidence interval, if many samples are collected and the confidence interval computed, in the long run about 95% of these intervals would contain the true mean.

From the Engineering Statistics Handbook [National Institute of Standards and Technology, Information and Technology Laboratory]