The average time it takes for a person to experience relief after taking a particular brand of medicine is at least 30 minutes. A new ingredient is added to help speed up relief. Let µ denote the average time to obtain relief with the new product. An experiment is conducted to verify if the new product is better. Which of the following is the most appropriate null and alternative hypotheses for this problem? A. Ho: μ ≥ 30 vs. Ha: μ < 30 B. Ho: μ < 30 vs. Ha: μ = 30 C. Ho: μ < 30 vs. Ha: μ > 30 D. Ho: μ ≤ 30 vs. Ha: μ > 30

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A new screening test for Lyme disease is developed for use in the general population. The sensitivity and specificity of the new test are 60% and 70%, respectively. Five hundred people are screened at a clinic during the first year the new test is implemented. Assume the true prevalence of Lyme disease among clinic attendees is 10%. Calculate the predictive value of a positive test.

Interpret a P-value: The manufacturer of a medication designed to lower blood pressure claims that the mean systolic blood pressure for people taking their medication is less than 135. To test this claim, blood pressure is measured for a sample of 500 people who are taking the medication. The P-value for testing Ho: μ = 135 versus H₁: µ< 135 is P = 0.001. a. The manufacturer concludes that because the P-value is very small, we can be fairly certain that the mean pressure is less than 135, but we cannot conclude that it is a lot smaller. Is this conclusion justified?

Assume that ρxy = .30 between weight and exercise for the population of normal adults. However, a researcher believes the relationship is stronger for children. The researcher tests a sample of 28 children and obtains an rxy = .47. Does this result support the researcher’s belief? Conduct an appropriate statistical test using an alpha level of .05.

The proportion of people who live after fighting cancer is 0.75. Suppose there is a new therapy that is used to increase the survival rate. Use the parameter p to represent the population portion of people who survive after fighting cancer. For a hypothesis test of the therapy’s effectiveness, researchers use a null hypothesis of p = 0.75. Pick the correct alternative hypothesis.  1. p > 0.75        2. p < 0.75          3. p 6= 0.75

If a treatment is expected to decrease scores in a population with µ= 30, then the alternative hypothesis is µ ≤ 30.  True or false?