Chapter 12 & 13 Activity Write up each test using the standard 5-step procedure. There is one of each of the following four tests: Goodness of Fit, Independence, ANOVA, Kruskal-Wallis 1) Does amount of education play a role in the healthiness of an individual? A random sample of individuals were asked to rate their health. Here are the results, broken down by level of education. Test the claim that health is independent of level of education at the 0.05 level of significance.
Excellent Good Poor Less Than High School 72 202 62 High School Grads 465 877 108 College Grads 439 561 25
Decision about H0:
Conclusion about H1:
2) A researcher plans soybeans in three types of plots: Liberty, No till, and Chisel plowed. The data represent the number of pods on a random sample of soybean plants for the three plot types. At the 0.05 level of significance, test the claim that the mean number of pods is the same for all 3 plot types. Plot Type Pods Liberty 32 31 36 35 41 34 39 37 38 No till 34 30 31 27 40 33 37 42 39 Chisel plowed 34 37 24 23 32 33 27 34 30
3) According to the manufacturer of M&Ms, 13% of the plain M&Ms in a bag should be brown, 14% yellow, 13% red, 24% blue, 20% orange, and 16% green. A student randomly selected a bag of plain M&Ms. He counted the number of M&Ms that were each color and obtained the results shown in the table. Test the claim that plain M&Ms follow the distribution stated by M&M/Mars at the 0.05 level of significance.
Color Brown Yellow Red Blue Orange Green Frequency 61 64 54 61 96 64
4) Here are the scores of randomly selected students on the Math 200, 230, and 21 finals. Use the 0.05 level of significance to test the claim that all 3 exams produce the same mean score. Math 200 38 42 55 64 73 80 95 Math 230 65 74 77 83 85 90 Math 21 80 82 85 89 94
- Chapter 12 & 13 Activity
Chapter 9 and 10 Activity This activity contains 2 confidence interval problems and 2 sample size problems from Chapter 9, along with 4 hypothesis tests from Chapter 10.
For confidence intervals, present your results in a sentence.
For each hypothesis test use the standard 5-step procedure. Two of the tests will fail their conditions, forcing you to use the alternative test:
• one-proportion (binomial) • one-mean (sign test)
1) Here are 10 randomly selected blood sugar levels from a laboratory. (Levels measured after a 12-hour fast in mg/DL.)
105 89 96 135 94 91 111 107 141 83
Use the data to test the claim that the mean blood sugar level is 100 mg/DL using the 0.05 level of significance.
2) A random sample of 400 college students were asked if they had experienced homelessness at any point in the last year, and 68 said that they had. Construct a 95% confidence interval for the proportion of all college students who have experienced homelessness at some point in the last year.
3) A college administrator wants to estimate the mean credit card debt of students at their school. How large of a sample is required in order to be 95% confident that their estimate is within $200 of the true population mean? The standard deviation of student credit card debt is believed to be approximately $2500.
4) A sample of 35 non-smokers revealed that 31 of them showed traces of a chemical that appears in the blood of people exposed to second-hand smoke. At the 0.05 level of significance test the claim that more than 80% of non-smokers are exposed to second-hand smoke.
5) A magazine article claims that more that 30% of college students own an iPhone. A random sample of 200 college students revealed that 72 of them own an iPhone. Test the magazine’s claim at the 0.05 level of significance.
6) A college administrator wants to estimate what percent of their students get the flu shot. How large of a sample will she need in order to be 90% confident that their estimate is within 4% of the true population proportion?
7) Eight artichoke plants at a farm were selected at random. Here are the number of artichokes produced by each plant last year.
38 32 17 51 40 36 34 39
At the 0.05 level of significance, test the claim that the mean number of artichokes is higher than 30 artichokes.
8) Sixty randomly selected COS students were asked how many units they were enrolled in this semester. The mean for the sample was 14.6 units, with a standard deviation of 4.2 units. Use this sample information to construct a 95% confidence interval for the mean number of units enrolled in by all COS students.
- Chapter 9 and 10 Activity
Math 21– Mashup for Chapters 9-11 These were the problems that you identified in the Math 321 Reading Assignment. Now work out each of the 9 problems. (HINT: One of the 5 hypothesis tests fails its conditions, and you will need to perform an alternate test.) For confidence intervals, write out our standard sentence. For hypothesis tests, use our standard 5-step procedure. 1) A nutritionist has developed a diet that she claims will help people lose weight. Twelve people were randomly selected to try the diet. Their weights were recorded prior to beginning the diet and again after 6 months. Here are the original weights, in pounds, with the weight after 6 months in parentheses.
Before 192 212 171 215 180 207 165 168 190 184 200 196 After 183 196 174 211 160 191 162 175 190 179 189 195
Test the claim that the diet is effective at the 0.05 level of significance. 2) A sample of 100 male drivers showed an annual mean of 10230 miles driven per year, with a standard deviation of 2870 miles. A similar sample of 28 female drivers showed an annual mean of 9660 miles driven per year, with a standard deviation of 2900 miles. Test the claim that the mean number of miles driven by male drivers is greater than the mean number of miles driven per year by female drivers at the 0.05 level of significance.
3) A researcher wants to determine what percent of high school students have asthma. How large of a sample does she need in order to be 95% confident that her estimate is within 6% of the true percentage of all high school students with asthma? 4) What proportion of all drivers turn on their headlights while driving in the rain? A sample of 200 vehicles on a rainy day showed that 41 had their headlights turned on. Test the claim that less than 25% of all drivers turn on their headlights while driving in the rain at the 0.01 level of significance.
5) A researcher wants to estimate the mean height of college-aged men. A sample of 50 college-aged men had a mean height of 70.6 inches and a standard deviation of 2.3 inches. Construct a 95% confidence interval for the mean height of all college-aged men. 6) A sample of 38 60-year-old smokers revealed that 10 of them have suffered with some sort of heart disease. A sample of 162 60-year-old nonsmokers showed that 12 of them have suffered with some sort of heart disease. At the 0.01 level of significance, test the claim that nonsmokers are less likely to suffer with some sort of heart disease by the time they turn 60 years old.
7) A researcher wants to estimate the mean student loan debt for students who graduate from a 4-year public university. How large of a sample does the researcher need to take in order to be 90% confident that the estimate is within $1000 of the mean debt for all graduates of a 4-year public university. Use a standard deviation of $8000. 8) A research team decides to estimate the percentage of college students who are married. A random sample of 2500 college student revealed that 175 of them were married. Construct a 95% confidence interval for the proportion of all college students who are married.
9) UPS monitors its trainees to see how fast they can work. A sample of 20 new employees handled a mean of 460.4 packages in one day, with a standard deviation of 38.83 packages. Test the claim that the mean number of packages handled per day by new employees is more than 450 packages, using the 0.05 level of significance.
- Math 21– Mashup for Chapters 9-11
Chapter 11 Activity
Data for Problems 3-6 can be found as ‘Chapter 11 Activity’ in the Woodbury Math 21 StatCrunch group.
1) Two Proportion Test In a study of 1054 people who were 60 or older, New York City researchers found that 19 of the 459 women and 11 of the 595 men had lung cancer. At the 0.01 level of significance, test the claim that men over 60 are less likely to get lung cancer than women over 60.
2) Two Proportion Randomization Test A research company conducted a survey in which they asked, “How many tattoos do you currently have on your body?”
• Of the 60 males surveyed, 9 responded that they had at least one tattoo. • Of the 110 females surveyed, 14 responded that they had at least one tattoo.
Test the claim that the proportion of males that have a tattoo is the same as the proportion of females that have a tattoo, at the 0.05 level of significance.
3) Paired Difference Test In a study of a new wonder diet, a sample of 10 patients was taken. Here are there weights before and after.
Before 209 178 169 212 180 192 158 180 211 193 After 196 171 170 207 177 190 159 180 203 183 Test at the 0.01 level of significance the claim that this diet is effective, in other words, that the diet will reduce the weight of a person.
4) Wilcoxon Signed Ranks Test To test the belief that sons are taller than their fathers, a student randomly selects 13 fathers who have adult male children. She records the height of both the father and son in inches and obtains the following data. Test the claim that sons are taller than their fathers at the 0.05 level of significance.
Father 70.3 67.1 70.9 66.8 72.8 70.4 71.8 70.1 69.9 70.8 70.2 70.4 72.4 Son 74.1 69.2 66.9 69.2 68.9 70.2 70.4 69.3 77.8 72.3 69.2 68.6 73.9
5) Two Mean Test A high school instructor is curious to see the effect that an open-notes policy would have on tests. He allows one of his classes to use their notes on their test, while his other class takes the test without them. Here are the scores.
With Notes 86, 95, 92, 93, 83, 84, 91, 83, 87, 85, 84, 77, 79, 74, 78
Without Notes 70, 72, 77, 60, 81, 97, 84, 61, 78, 98, 68, 53, 69, 84, 91, 78
At the 0.05 level, test the claim that the use of notes produces a higher mean test score.
6) Mann Whitney Test A researcher plans soybeans in two types of plots: “No till” and “Chisel plowed”. The data represent the number of pods on a random sample of soybean plants for the two plot types.
Plot Type Pods No till 34 30 31 27 40 33 37 42 39 Chisel plowed 34 37 24 23 32 33 27 34 5 At the 0.05 level of significance, test the claim that the mean number of pods for “Chisel plowed” is less than “No till”.