Additional Attachment

Name: _________________________________________ Math 21 Final Exam – Part 1 Spring 2021 Upload to Canvas Due by midnight on Wednesday May 19 – no exceptions.

What do I need to write? • Sample Size Problems: Just state the minimum sample size.

• Confidence Intervals: State your result is a sentence, like “We are 95% confident that

____________ is between ____________ & __________ .”

• Hypothesis Tests: Perform the appropriate hypothesis test, including all 5 steps. o H0 & H1 o α o Test o Test Statistic/p-value o Decision about H0/Conclusion about H1

Alternative Tests

• If the necessary conditions are not met, use the appropriate alternative test. o One Proportion – Binomial o Two Proportion – Randomization Test for Two Proportions o One Mean – Sign Test o Paired Difference – Wilcoxon Signed Ranks o Two Mean Test – Mann Whitney o ANOVA – Kruskal Wallis

1) A doctor claims that less than 75% of the patients that he performs a knee replacement surgery on return to work in the first 3 months after the operation. A sample of 50 patients that had a knee replaced by the doctor showed that only 34 of them returned to work within 3 months of the surgery. Test the doctor’s claim at the 0.05 level of significance. 2) A researcher wants to determine what proportion of all high school students plans to attend community college upon graduating. He has no idea of what the sample proportion will be. How large of a sample is required in order to be 90% sure that the sample proportion is off by no more than 2%?

3) In a survey of 500 college students, 58 of them were left-handed. Construct a 90% confidence interval for the proportion of all college students who are left-handed. 4) Researchers wanted to analyze daily calcium consumption by children based on the types of meat they eat. The data represent the daily consumption of calcium (in mg) of 8 randomly selected children from each of three groups: those who only eat lean meats, those who eat a mixture of lean and higher-fat meats, and those who only eat higher-fat meats.

Lean Meats Mixed Meats Higher-Fat Meats 844.2 897.7 843.4 745.0 908.1 862.2 773.1 948.8 790.5 823.6 836.6 876.5 812.0 871.6 790.8 758.9 945.9 847.2 810.7 859.4 772.0 790.6 920.2 851.3

At the 0.05 level of significance, test the claim that the mean calcium consumption for all 3 categories is the same.

5) A local tutorial franchise offers an SAT Prep course. Students begin by taking a pre-test. After taking the course, students take the SAT. Here are the results for 8 randomly selected students.

Student A B C D E F G Pre-Test 960 870 980 1250 1100 1210 1460 SAT 1090 950 1140 1300 990 1360 1530

At the 0.05 level of significance, test the claim that the Prep course produces an overall increase in scores. 6) A random sample of 506 registered voters were asked about their own political ideology (progressive/moderate/conservative) and whether they felt that the country was heading in the right direction or if it was on the wrong track. Here are the results.

Opinion Progressive Moderate Conservative Right Direction 84 48 32

Wrong Track 90 118 134 At the 0.05 level of significance, test the claim that political ideology and response about the direction the country is heading are independent.

7) A random sample of 500 Spanish adults revealed that 180 were smokers. A random sample of 265 American adults revealed that 55 were smokers. At the 0.05 level of significance, test the claim that the proportion of Spanish adults that smoke is greater than the proportion of American adults that smoke. 8) To test the claim that the mean blood glucose level of senior citizens is 100 mg/dL, a researcher takes a random sample of 48 senior citizens. They had a mean blood glucose level of 115.6 mg/dL, with a standard deviation of 32.8 mg/dL). Test the claim at the 0.05 level of significance.

9) Here are the final exam scores of 9 randomly selected students on a Math 21 exam. 62 68 73 75 78 80 83 88 94

Construct a 95% confidence interval for the mean final exam score for all Math 21 students. 10) Here are the scores of eight Math 21 students on their midterm exam and their final exam.

Student 1 2 3 4 6 7 8 Midterm 74 71 85 80 78 71 88 Final 83 77 100 90 89 80 96

Use the 0.05 level of significance to test the claim that Math 21 students improve their scores from the midterm exam to the final exam.

11) A random sample of 40 COS students contained 11 that owned an iPhone. A random sample of 150 Fresno State students contained 53 that owned an iPhone. Use these data to test the claim that the proportion of COS students who own an iPhone is the same as the proportion of Fresno State students who own an iPhone at the 0.05 level of significance. 12) Eleven statistics students and twelve algebra students were asked how many hours they studied for their final. Here are their responses. Statistics

8 10 12 7 9 13 8 10 14 10 9 Algebra

6 7 5 8 10 6 8 5 0 11 9 6 At the 0.05 level of significance, test the claim that the mean number of hours studied by Math 21 students is greater than the mean number of hours studied by Math 200 students.

13) Here are the scores of randomly selected Math 200, Math 230, and Math 21 students on their final exams. Math 200 38 51 59 70 82 86 99 Math 230 70 75 80 80 84 90 94 Math 21 92 94 95 95 96 98 100 Test the claim that the mean final exam score is the same for all three classes at the 0.05 level of significance. 14) A company makes tortilla chips in two locations: Los Angeles and Oakland. A random sample of 60 bags made in Los Angeles had a mean weight of 11.08 ounces, with a standard deviation of 0.07 ounces. A random sample of 40 bags made in Oakland had a mean weight of 11.03 ounces, with a standard deviation of 0.11 ounces. At the 0.05 level of significance, test the claim that the mean weight of tortilla chip bags is the same for both locations.

15) A random sample of 300 college graduates were asked how much student debt they had upon graduation. The mean debt was $11,625, with a standard deviation of $9600. Construct a 99% confidence interval for the mean amount of student debt at graduation for all college graduates. 16) A random sample of 200 Fresno State students revealed that 114 were female. Test the claim that more than 50% of Fresno State students are female using a 0.05 level of significance.

17) Test the claim that the mean time required for high school students to run 1 mile is greater than 7 minutes at the 0.05 level of significance. Here are the results of a random sample of 25 students.

7.3 7.7 9.2 8.8 7.6 7.2 6.6 6.4 8.0 7.3 7.8 8.2 10.4 11.6 7.2 7.7 7.0

18) The president of a college wants to determine the mean number of units that college students take per semester. How large of a sample is required in order to be 95% sure that a sample mean will be off by no more than 0.5 units? An initial study suggested that the standard deviation is approximately 4.3 units.

19) Five years ago, 45% of registered voters were in favor of Medicare For All, 35% were opposed, and 20% were unsure. This year, a survey of 800 randomly selected registered voters showed that 412 were in favor, 317 were opposed, and 71 were unsure. At the 0.05 level of significance, test the claim that the proportions for all voters have stayed the same as they were 5 years ago. 20) A random sample of 8 hybrid cars had the following highway mileages in mpg. 36 41 37 45 50 40 32 39 Test the claim that the mean highway mileage for hybrid cars is above 35 mpg at the 0.05 level of significance.