Suppose the incidence rate of influenza (flu) during the winter of 1998-1999 (i.e. from December 21, 1998 to March 20, 1999) was 50 events per 1000 person-months among students in high schools in a particular city. Among 1200 students in one high school in the city, 200 developed a new case of influenza over the winter of 1999-2000 (i.e. the 90 days from December 21, 1999 to March 20, 2000).

Question: Test the hypothesis that the rate of flu has changed from winter 1998-1999 to winter 1999-2000. Write
out all 4 steps of the hypothesis test including a two-tailed p-value.

The time needed to complete a final examination in a particular college course is normally distributed with a mean of 83 minutes and a standard deviation of 13 minutes. Answer the following questions. Round the intermediate calculations for z value to 2 decimal places. Use Table 1 in Appendix B. What is the probability of completing the exam in one hour or less (to 4 decimals)? What is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes (to 4 decimals)? Assume that the class has 60 students and that the examination period is 90 minutes in length. How many students do you expect will be unable to complete the exam in the allotted time (to the next whole number)?

between-subjects t-test

A math teacher was interested in determining performance as a function of time of day during morning and evening classes. He recruited twenty students to participate: 10 were randomly assigned to participate in the morning class (8am), and the other 10 students were assigned to the afternoon class (3pm).

Data Set:

From past experience, Dr. R-P believes that the average score on a Research Methods Course is 75. A sample of 10 students exam scores is as follows:
80, 68, 72, 73, 76, 81, 71, 71, 65, 53.
Test the claim that the students average is still 75. Use α = 0.01. [You need to first compute the mean and the standard deviation, then the standard error from your sample. To do this, use the computational method for ungrouped data that we learned in chapter 5, page 128-129. (Show all your work; this gives you a complete view of where all these numbers we use in hypothesis testing or confidence interval come from)].

In a school district, all sixth grade students take the same standardized test. The superintendant of the school district takes a random sample of 22 scores from all of the students who took the test. She sees that the mean score is 160 with a standard deviation of 28.2396. The superintendant wants to know if the standard deviation has changed this year. Previously, the population standard deviation was 28. Is there evidence that the standard deviation of test scores has increased at the α=0.005 level? Assume the population is normally distributed. Step 2 of 5 : Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer to three decimal places.

Breathing rates for humans can be as low as 4 breaths per minute or as high as 70 or 75 for a person doing strenuous exercise. Suppose that the resting breathing rates for college-age students have a distribution that is mound-shaped, with a mean of 12 and a standard deviation of 2.3 breaths per minute. What fraction of all students have breathing rates in the following intervals.

a. 9.7 to 14.3 breaths per minute

b. 7.4 to 16.6 breaths per minute

c. More than 18.9 or less than 5.1 breaths per minute

Please explain how every number was solved/or found, please. I'm very confused about how this should be solved.

The Scholastic Aptitude Test (SAT) contains three parts: critical reading, mathematics, and writing. Each part is scored on an 800-point scale. A sample of SAT scores for six students follows.

a. Using a  level of significance, do students perform differently on the three portions of the SAT?

Several years ago, 41% of parents who had children in grades K-12 were satisfied with the quality of education the students receive. A recent poll asked 1115 parents who have children in grades K-12 if they were satisfied with the quality of education the students receive. Of the 1115 surveyed, 452 indicated that they were satisfied. Perform an appropriate hypothesis test to assess whether this represents evidence that parents' attitudes toward the quality of education have changed. Use \alpha=0.05α=0.05 level of significance.

1 - Check requirement and state the hypotheses.

2 - Round test statistic to 3 decimals, and p-value to 4 decimals.

3 - State your conclusion in a complete sentence.

1. A survey of 200 students is selected randomly on a large university campus They are asked if they use a laptop in class to take notes. The result of the survey is that 70 of the 200 students use laptops to take notes in class.
   1. What is the value of the sample proportion? (0.5 pts)
      
   2. What is the standard error of the sampling proportion? (0.5 pts)
      
   3. Construct an approximate 95% confidence interval for the true proportion by going 2 standard errors from the sampling proportion. (1 pt)
      
   4. How would the confidence interval have changed if the confidence level was 90% instead of 95%? (1 pt)
      
   5. How would the confidence interval have changed if the sample size had been 100 instead of 200? (1 pt)
      

Decisions about alpha level may be different, especially as it relates from hard sciences to social sciences. For example, a medical trial for cancer treatments conducts their statistical tests at .0001 - so for every 1 out of 10,000 patients, there may be issues, sickness or even death. For social science, we use alpha .05. We are comfortable with performing research, for example, on students. So we are satisfied with losing 5 out of 100 students or having our results being incorrect 5 out of 100 times. Do you agree with these alpha levels? Why or why not? What if your child's education and the teacher assigned to him/her would be successful 95 out of 100 times?