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Additional Example from Section 9.7 (Math 12, Fall 2021)

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Section 9.7 PowerPoint, Math 12 (Fall 2021)

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Section 9.7--Test of Independence (Math 12 Fall 2021)

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Section 9.6 on Experiments with Goodness with Goodness of Fit Tests

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Section 9.6 on Experiments with Goodness with Goodness of Fit Tests

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Section 9.6--Experiment with Goodness of Fit Tests (Math 12 Fall 2021)

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Section 9.6 on Goodness of Fit Tests (Math 12 Fall 2021)

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Section 9.5 on Regression (Math 12 & 112 Fall 2021)

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Graphing Lines Practice (Math 12 & 112 Fall 2021)

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Section 9.4 on Linear Correlation (Math 12 & 112 Fall 2021)

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Section 9.2 on One-Way ANOVA (Math 12 & 112 Fall 2021)

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Section 9.1 PowerPoint, Math 12 (Fall 2021)

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Section 9.1 on Foundations of Advanced Hypothesis Testing (Math 12 & 112 Fall 2021)

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Test 3 is a take-home test. I gave copies of the test in class on Tuesday Nov. 9. If you did not get a copy of test, please print out your own copy. The test is due in class on Tuesday November 16.

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Math 12--Statistics
Review for Test 3 on Chapter 8

Expect 1 or 2 questions from Sections 8.2 through 8.4 and at least 1 question each from Sections 8.5 through 8.8 on the test.

We have covered the following types of hypothesis tests in Chapter 8:

Section 8.2 on Hypothesis Tests for One Proportion
Section 8.3 on Hypothesis Tests for One Mean
Section 8.4 on Hypothesis Tests for One Standard Deviation or Variance
Section 8.5 on Hypothesis Tests for Two Proportions
Section 8.6 on Hypothesis Tests for Two Means from Independent Samples
Section 8.7 on Hypothesis Tests for the Mean of Differences
Section 8.8 on Hypothesis Tests for Two Standard Deviations or Variances

The following questions are based on the questions from Section 8.9 of the book on pages 273 to 275.

1.) 30 Statsville residents and 35 Wudmoor residents were asked, "What is the biggest challenge you face when it comes to exercising?" 70% of the Statsville respondents answered, "Time" as did 89% of the Wudmoor respondents. A local gym owner believes that a greater proportion of Wudmoor residents have time as their greatest exercise challenge than Statsville residents who feel this way. Test the gym owner's belief.

2.) A computer technician wants to see if a certain maintenance process reduces the variation in the luminosity of computer monitors. 12 randomly selected computer monitors were tested using this process and their luminosity, in candelas per square meter, were recorded below. Perform an appropriate hypothesis test to determine if the variation of the luminosity of computer monitors that undergo this process is less than 50 candelas per square meter.

402
437
408
408
354
368
411
352
425
416
406
395

3.) A sample of 376 people was asked what they find amusing. "Dark Humor" was a response from Homer, Marge, Bart, Lisa, and 192 others. Can we conclude that most people find dark humor amusing? Perform an appropriate hypothesis to answer this question.

4.) In a recent survey, 93% of Statsville Medical Group patients reported feeling listened to and respected by their doctor. On this matter, 89% of Wudmoor Medical Group patients expressed the same sentiment. During observations of 17 visits from Statsville Medical Group patients, doctors allowed patients an average 16.1 seconds to explain the reason for their visit before the doctor interrupted. During observations of 11 visits from Wudmoor Medical Group patients, doctors allowed patients an average of 12.2 seconds to explain the reason for the visit before the doctor interrupted. The variances for each group of observations were 12.96 seconds squared and 7.29 seconds squared, respectively. Does it appear that doctors at Statsville Medical Group typically allow their patients more time to talk than doctors at Wudmoor Medical Group? Perform an appropriate hypothesis test using 0.10 level of significance.

5.) Dental experts recommend that people spend two minutes, per session, brushing their teeth. A dental hygienist asked 32 patients to time themselves when they brush their teeth at home. Each person used a stopwatch to record the actual time, in sections, spent brushing. These patients also recorded how long they thought they brushed during these sessions. On average, the patients brushed for 20 fewer seconds, with a standard deviation of 11.4 seconds, than they thought they did. Do people in general not brush for as long as they believe they do? When performing the appropriate hypothesis test, we want the probability of incorrectly answering "yes" to this question to be 0.05.

6.) A kinesiologist in Wudmoor is wondering about how much people walk in Statsville compared to Notmoovin. The kinesiologist outfitted 20 randomly selected residents from Notmoovin and 54 randomly selected residents from Statsville with devices to monitor their steps for one day. The kinesiologist gave instructions to the participants of this study, including the fact that they should go about their usual behavior. The participants from Statsville walked an average of 10937 steps with a standard deviation of 1378. The data for the 20 participants from Notmoovin is below. Using a significance level of 0.01, test the claim that the dispersion of the daily steps walked by Notmoovin residents is greater than the dispersion of daily steps walked by Statsville residents.

2519
6269
6608
9666
7634
6447
4443
2596
8865
6262
4414
10248
7517
10710
3396
6261
13474
11857
5649
5992

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Study Guide for Test 3 on Chapter 8 (Math 12 Fall 2021)

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Section 8.8 PowerPoint, Math 12 (Fall 2021)

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Section 8.6 PowerPoint, Math 12 (Fall 2021)

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Section 8.5 PowerPoint, Math 12 (Fall 2021)

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Section 8.4 PowerPoint, Math 12 (Fall 2021)

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Section 8.3 PowerPoint, Math 12 (Fall 2021)

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More About the Traditional and P-value Methods of Hypothesis Testing

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More About the Traditional and P-value Methods of Hypothesis Testing

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Chapter 8: Basic Hypothesis Testing

How do we know whether to reject or fail to reject the null hypothesis?

For the Traditional Method, we must find the critical values and identify the rejection region or regions of the test.

If the < symbol is used in the alternative hypothesis, then the test is called a left-tailed test. This means the rejection region is in the left tail of the probability distribution. There is only one critical value for left-tailed tests.

If the > symbol is used in the alternative hypothesis, then the test is right-tailed. The rejection region will be in the right tail of the probability distribution. There is only one critical value for right-tailed tests.

If the not equal symbol is used, then we have a two-tailed test. There are two rejection regions, one in the left tail and the other in the right tail. Therefore, there are two critical values for two-tailed tests.

The critical values are the cut-off values that help us determine whether a test statistic is in the rejection region. Once we have our test statistic, we then find the critical value(s).

The total area inside the rejection region is always equal to the significance level of our test.

*For left-tailed tests, the area to the LEFT of the critical value is alpha.
*For right-tailed tests, the area to the RIGHT of the critical value is also alpha.
*For two-tailed tests, there are two rejection regions, one on the left and the other on the right. If the total area is alpha, then half the value of alpha is in the left-tail and half value of alpha is in the right-tail.

Therefore, when finding the critical values for two-tailed tests, divide the significance level by 2 to get the correct area in each tail.

Remember to use the appropriate function to get the critical values:

*invNorm( to find critical values from the z-distribution, also known as the standard normal distribution. The standard normal distribution has a mean of 0 and standard deviation of 1.

*INVT or invT( to find critical values from the t-distribution, also know as Student's t-distribution. Remember to enter the correct degrees of freedom.

*INVCHI2 to find critical values from the chi-square distribution. Remember to enter the correct degrees of freedom.


If the test statistic is inside the rejection region, REJECT the null hypothesis.
If not, DO NOT REJECT the null hypothesis.


For the P-value Method, use your calculator to find the P-value of the test. Then compare the P-value to the significance level.

If the P-value is smaller than alpha, REJECT the null hypothesis.
If the P-value is greater than or equal to alpha, DO NOT REJECT the null hypothesis.


Both the P-value Method and Traditional Method will lead to the same conclusion in a hypothesis test!

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Null Hypothesis Decision Summary (Math 12 Fall 2021)

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Answer Key to Study Guide for Test 2 (Math 12 Fall 2021)

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Math 12--Statistics
Review for Test 2 on Chapter 7

Expect 2 questions from Sections 7.2 through 7.4 and at least 1 question each from Sections 7.5 through 7.8.

We have covered the following types of confidence intervals in Chapter 7:

Section 7.2 on Confidence Intervals for One Proportion
Section 7.3 on Confidence Intervals for One Mean
Section 7.4 on Confidence Intervals for One Standard Deviation or Variance
Section 7.5 on Confidence Intervals for Two Proportions
Section 7.6 on Confidence Intervals for Two Means
Section 7.7 on Confidence Intervals for the Mean of Differences
Section 7.8 on Confidence Intervals for the Ratio of Two Variances or Standard Deviations

1.) Moviegoers were asked their favorite soft drink. 14 chose Popsee and 58 chose something else. Create a 99 % confidence interval for the proportion of movie goers who prefer Popsee. Round your confidence interval limits to 3 decimal places.

2.) Use your confidence interval from the previous question to test the claim that more than half of movie goers prefer Popsee. Does this claim appear to be true? Briefly explain why or why not.

3.) The same movie goers in Question 1 who preferred Popsee were observed during their stay in the movie theater on day they were interviewed. They stayed at the theater an average of 145.6 minutes with a variance of 600.3 minutes squared. Use this information to create a 90% confidence interval for the average amount all movie goers who prefer Popsee spend at the theater. Round your confidence interval limits to the nearest tenth.

Hint: The square root of the variance is equal to the standard deviation.

4.) The manager of a local movie theater wants to estimate the proportion of moviegoers who buy popcorn at their visit to the movie theater. What is the smallest number of moviegoers he needs to survey to make an estimate that is within 0.07 of the true proportion with 87% confidence? Round your final answer up to the nearest whole number.

5.) Is there some connection between plant growth and music? There are varying opinions on this question, even among those who have performed research in this area. A botanist observed the growth of plants in an environment where rock music is played, as well as plants in an environment where classical music is played. All other aspects of the environment--soil, sunlight, frequency and amount of watering, etc.--were identical. The botanist used a quantitative measure for the plants that included features like amount of growth, thickness, color, and other aspects of plant health. A higher value indicates better plant growth. The 31 plants grown in the rock music environment had a mean of 147.23 with standard deviation of 38.60 on the quantitative measure, and the 25 plants grown in the classical music environment had a mean of 195.11 with a standard deviation of 18.10. Use a 95% confidence interval to see if, using this quantitative measure, plants grown in classical music grow more on average than plants grown in rock music. Round your confidence interval limits to the nearest tenth and respond to the research question.

6.) Gepher insurance company claims that people save an average of 15% or more on car insurance when switching to Gepher. Below are the annual car insurance premiums for a random selection of customers who switched to Gepher. The annual car insurance premiums with their previous insurance company are in the first column and their current insurance premiums with Gepher are in the second column. Create a 90% confidence interval to address the claim that customers who switch to Gepher save money on their car insurance.

Previous Company Gepher
$1389.26         $1041.67
$1641.17         $1380.22
$912.84          $832.51
$1213.22         $912.34
$1693.47         $1386.95
$2014.88         $1567.58
$1101.96         $715.06

7.) Randomly selected international arrivals to JFK airport and randomly selected international arrivals into SFO airport experienced wait times, in minutes, going through customs as shown in the table below. Use a 98% confidence interval to address the claim that the wait-times to go through customs at JFK airport are more varied that the wait-times to go through customs at SFO airport. Round your confidence interval limits to 3 decimal places and respond to the claim.

JFK  SFO
20.0 27.9
28.4 26.8
52.0 18.4
15.5 25.9
17.1 27.2
30.0 36.8

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Study Guide for Test 2 on Chapter 7 (Math 12 Fall 2021)

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Section 7.8 PowerPoint, Math 12 (Fall 2021)

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Section 7.7 PowerPoint, Math 12 (Fall 2021)

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Section 7.6 PowerPoint, Math 12 (Fall 2021)

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Section 7.5 PowerPoint, Math 12 (Fall 2021)

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Section 7.4 PowerPoint, Math 12 (Fall 2021)

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Section 7.1 PowerPoint, Math 12 (Fall 2021)

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Chapter 6 on Inferential Statistics Ideas, Math 12 (Fall 2021)

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Chapter 6 Handout (Math 12 & 112 Fall 2021)

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Section 5.3 PowerPoint, Math 12 (Fall 2021)

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Section 5.2 PowerPoint, Math 12 (Fall 2021)

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Section 5.1 PowerPoint, Math 12 (Fall 2021)

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Chapter 4 Handout (Math 12 & 112 Fall 2021)

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Click to see a list of topics that will be on the quiz. The quiz will be given at the beginning of class on Tuesday September 7 after I collect your homework from Chapter 2.

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Here is a lists of topics that are likely to be on Tuesday's Quiz

1.) Create a frequency table for a data set given the lower class limit of the first class and the class width. Fill in the class limits and frequencies for each class in your table.

2.) Find the relative frequency and cumulative frequency for each class in your table.

3.) Draw a frequency histogram for the same data set. You may use your calculator to do this, but you must draw your graph by hand. Be sure to label the axes in your graph appropriately.

4.) Know how to do the following other graphs. You will be asked to create one of these graphs on the quiz.
a. Stem-and-leaf plots
b. Dot plots

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Topics for Chapter 2 Quiz, Math 12 Fall 2021

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This handout contains some of the examples from Chapter 2 of the textbook. We will go over this in class and you do not need to turn it in.

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Math 12 Examples from Chapter 2 of Book, Fall 2021

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This worksheet lists various examples of data. You are asked to classify each data type as quantitative or qualitative and as discrete or continuous. We went over this worksheet in class last week. You do not need to turn it!

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Chapter 1 Quiz Practice on Identifying Data Types, Math 12 & 112 Fall 2021

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A copy of the syllabus scavenger hunt we went over during the first week of class.

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Syllabus Scavenger Hunt for Math 12 & 112, Fall 2021 (RCC)

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Here is an extra copy of the syllabus in case you need it.

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Click above to get back to the homework page.