Recently, mumps outbreaks have become more common, with many occurring among individuals 18-24 years of age living on college campuses. Two doses of the measles-mumps-rubella (MMR) vaccine are recommended for protection from mumps. Herd immunity refers to the proportion of individuals that must be immune to effectively prevent the spread of disease through a population. In order to prevent the spread of mumps, at least 96% of people in a community must have received two doses of the MMR vaccine.

a) Suppose that 94% of undergraduate students in the United States report having received two doses of the MMR vaccine. What is the probability that in one upperclassman House at MIT, enough students are vaccinated to achieve herd immunity? There are approximately 400 students in any house.

b) Calculate the probability that herd immunity is achieved in all 12 Houses.

c) Discuss the validity of the assumptions required to make the calculation in part i.

::Here is data:: about students in our class showing what country they are from and their opinion about pineapple on pizza.  

https://docs.google.com/spreadsheets/u/3/d/1a5nXmzTGaF_knVmvDkOrSQhpRfEp6edUXm1e7Ze-1_M/edit?usp=sharing

Conduct a hypothesis test to compare the proportion of Shoreline students who love pineapple on pizza (answered “YEAH!” on the survey) who are from Asia and the proportion of students who love pineapple on pizza who are from North America.

For each of the steps below, explain your work in words, symbols, and pictures.

1. Write the null and alternative hypotheses in words and symbols.

2. Check the conditions necessary to use the Central Limit Theorem.

3. Select an alpha level and use it to find the critical values.

4. Find your test statistic and compare it to the critical values.

5. Compute the p-value of your test statistic and compare it to alpha.

6. Describe what the p-value measures in this hypothesis test.

7. Make a decision about the null hypothesis.

8. Interpret that decision.

Perform the following hypothesis test using the critical value (traditional) method. Be sure to state the null and alternative hypotheses, identify the critical value, calculate the test statistic, compare the test statistic to the critical value, and state the conclusion. Use English if you cannot write the mathematical symbols. A psychologist is interested in exploring whether or not male and female college students have different driving behaviors. She opted to focus on the fastest speed ever driven by an individual. Therefore, the particular statistical question she framed was as follows: Is the mean fastest speed driven by male college students different than the mean fastest speed driven by female college students? A sample of 34 men had a mean speed of 105.5 mph with a standard deviation of 20.1 mph, while a sample of 29 women had a mean speed of 90.9 mph with a standard deviation of 12.2 mph. Use α = .05 and assume that population variances are equal.

1. Seven hundred and seventy-one distance learning students at Long Beach City College, located in Long Beach, California (part of the Los Angeles metropolitan area) responded to surveys in the 2010-11 academic year. Highlights of the summary report are listed in the table below:

1. What percent of the students surveyed do not have a computer at home?
2. About how many students in the survey live at least 16 miles from campus?
3. If the same survey were done at Great Basin College in Elko, Nevada, do you think the percentages would be the same? Why?

A study of the ages of motorcyclists killed in crashes involves the random selection of 132

drivers with a sample mean of 32.95 years. Assume that the SAMPLE standard deviation is 9.4 years. a) Find the critical value tα /2 for a 90% confidence interval

b) Construct and interpret the 90% confidence interval estimate of the mean age of all motorcyclists killed in crashes. Use the z-table method.

dence interval.

Question 2. Randomly selected statistics students of the author participated in an experiment to test their ability to determine when 60 seconds has passed. Forty students yielded a sample mean of

57.3 sec. Assume that the sample standard deviation is σ = 8.5 sec.

1. a) Find the critical value tα /2 for a 80% confidence interval

2. b) Construct a 80% confidence interval estimate of the population mean of all statistics students. Use the z-table method.

3. c) Use TI84/83 calculator method.

4. d) Write a conclusion.

The National Center for Education Statistics found that in 2015, 41% of students nationwide reported that their mothers had graduated from college. A superintendent randomly sampled 356 students from her local school district and found that 43% of them had mothers that graduated from college. Does her sample give evidence of a higher education level among mothers in her district? Use a significance level of ? = 0.05.

a) State the hypotheses in symbols.   

b) Run the test and report the test statistic and p-value. Be sure to write out what you entered in your calculator.

c) Write a full conclusion for this test in the context of the problem (see #2b for format).   

d) Find a 90% confidence interval for the proportion of students in the superintendent’s district that have mothers who graduated from college. Be sure to write out what you entered in your calculator.

e) Does this confidence interval support your conclusion in part (c)? Explain.

In a study of academic procrastination, the authors of a paper reported that for a sample of 431 undergraduate students at a midsize public university preparing for a final exam in an introductory psychology course, the mean time spent studying for the exam was 7.24 hours and the standard deviation of study times was 3.50 hours. For purposes of this exercise, assume that it is reasonable to regard this sample as representative of students taking introductory psychology at this university.

(a) Construct a 95% confidence interval to estimate μ, the mean time spent studying for the final exam for students taking introductory psychology at this university. (Round your answers to three decimal places.)

(b) The paper also gave the following sample statistics for the percentage of study time that occurred in the 24 hours prior to the exam.

n = 431      x = 43.18      s = 21.26

Construct a 90% confidence interval for the mean percentage of study time that occurs in the 24 hours prior to the exam. (Round your answers to three decimal places.)
(  ,  ) ( , )

3) Scores on the verbal Graduate Record Exam (GRE) have a mean of 462 and a standard deviation of 119. Scores on the quantitative GRE have a mean of 584 and a standard deviation of 151. Assume the scores are normally distributed.

a) Suppose a graduate program requires students to have verbal and quantitative scores at or above the 90th percentile. What is the verbal score (to the whole point) required? (1 point)

b) What is the quantitative score required at or above the 90th percentile? Round to the whole point. (1 point)

c) A perfect score on either exam is 800. What percentage of students score 800 on the verbal exam? Round to the hundredths of a percent as needed. (1 point)

d) A perfect score on either exam is 800. What percentage of students score 800 on the quantitative exam? Round to the tenths as needed. (1 point)

e) If someone scored higher than 2.5% of the quantitative test takers, what is that score?

You have been given the task of finding out what proportion of students that enroll in a local university actually complete their degree. You have access to first year enrolment records and you decide to randomly sample 115 of those records. You find that 87 of those sampled went on to complete their degree.

a)Calculate the proportion of sampled students that complete their degree. Give your answer as a decimal to 3 decimal places.

Sample proportion =

You decide to construct a 95% confidence interval for the proportion of all enrolling students at the university that complete their degree. If you use your answer to part a) in the following calculations, use the rounded version.

b)Calculate the lower bound for the confidence interval. Give your answer as a decimal to 3 decimal places.

Lower bound for confidence interval =

c)Calculate the upper bound for the confidence interval. Give your answer as a decimal to 3 decimal places.

Upper bound for confidence interval =

1. Suppose we measure the heights of 40 randomly chosen statistics students. We find a mean height of 175cm. Since we have a sufficiently large sample, let’s just assume that the sample standard deviation is the same as the population standard deviation = 20cm.

1. Construct a 95% confidence interval for the population mean height of statistics students AND write a sentence interpreting your results.
2. Construct a 99% confidence interval for the population mean height of statistics students AND write a sentence interpreting your results.

2. There are hundreds of apples on the trees (seriously, this was supposed to be a nice fall example, then it snowed!), so you randomly pick 46 apples and get a mean circumference of 86 and a standard deviation of 6.2 mm.

1. Construct a 90% confidence interval for the size of the apples and write a sentence interpreting your result.

2. If the orchard’s contract with Pick-n-Save states that apples must be 88mm in circumference or larger, are you in trouble? Explain.