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Migraine and Acupuncture: A migraine is a particularly painful type of headache, which patients sometimes wish to treat with acupuncture. To determine whether acupuncture relieves migraine pain, researchers conducted a randomized controlled study where patients diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control. Patients in the treatment group received acupuncture that is specifically designed to treat migraines. Patients in the control group received placebo acupuncture (needle insertion at non-acupoint locations). 24 hours after patients received acupuncture, they were asked if they were pain free. Results are summarized in the contingency table below. The goal is to see if there is an association between receiving the treatment and experiencing pain. Use the table to determine the expected number of people who were pain free and actually had the treatment. Round your answer to the nearest hundredth. Data table Pain Free: Yes Pain Free: No Treatment [a] [b] Control [c] [d]   Click here to open a Numworks Calculator

A student scores [x] on an exam where the mean is [mu] and the standard deviation is [s]. To two decimal places, what is the student’s z-score? Click here to open a Numworks Calculator

A hypothesis test is conducted to test the claim

How many hours do full-time students work outside of school in a typical week?  A study of 60 individuals reported, among many other things, Q1 = 8 and Q3 = 20.  Which of these statements must be true? 

The mean amount of coffee consumed in a week is found to be approximately normally distributed with a mean of 36 ounces and a standard deviation of 4 ounces. According to the Empirical rule, about what percentage of people consume between 28 and 44 ounces?  Click here to open a Numworks Calculator

Does the number of hashtags in a post help to increase its popularity? A random sample of hundreds of posts with varying numbers of hashtags was collected along with the number of likes on that post. The regression equation for this study was found to be  ŷ = 540 + 1892x.  What does the slope of this regression line represent? 

A 95% confidence interval for the proportion of Southwest Washingtonians who are in favor of a light rail service is ([p1], [p2]). To three decimal places, what is the margin of error?  Click here to open a Numworks Calculator

In hypothesis testing, the null hypothesis (H₀) typically represents:

A 95% confidence interval for the true mean length of time for full-time college students to complete a bachelor’s degree is ([a], [b]). To the nearest hundredth, what is the point estimate for the population mean?  Click here to open a Numworks Calculator

A magazine asks readers to mail in their opinions about gun control. The results are likely to suffer from: