1. Diagnosing stroke strictly on the basis of clinical symptoms is difficult. One method for diagnosing stroke measures cerebral blood flow (CBF) in the brain because stroke patients tend to have lower CBF levels than normal. Assume that in the general population, CBF is normally distributed with a mean of 75 mL/100 g brain tissue and a standard deviation of 17 mL/100 g brain tissue. A patient is classified as being at risk for stroke if his or her CBF is lower than 45 mL/100 g brain tissue, and a patient is classified as being at severe risk for stroke if his or her CBF is lower than 40 ml/100 g brain tissue. a. What is the probability that a patient will have a CBF between 45 ml/100 g brain tissue and 75 ml/100 g brain tissue? b. What is the probability that a patient will have a CBF greater than 45 ml/100 g brain tissue? c. What is the probability that a patient will have a CBF less than 40 ml/100 g brain tissue? d. What is the probability that a patient will have a CBF between 40 ml/100 g brain tissue and 45 ml/100 g brain tissue?

2. A Dr. believes that the average time she spends with a patient at her clinic for an appointment is 9 minutes with an average standard deviation of 1.5 minute. In order to test if the average time spent with a patient is 9 minutes, a random sample of 85 patient appointment times are recorded over the past month, and a mean appointment time was 9.2 minutes. Test the hypothesis that the mean appointment time is equal to or less than 9 minutes at the 0.05 level of significance. H0: 9 minutes H1: > 9 minutes

3. In a certain town, it is assumed that the mean bone density score (T score) for seniors aged 70 - 75 is -0.7 with a standard deviation of 1.3. A sample of 92 seniors aged 70 - 75 was selected to have bone density tests. What is the probability that: a. The sample mean T score is less than -1.0? b. The sample mean T score is between -1.0 and -0.8?

4. In a certain town, a research group is trying to discover how many seniors, aged 65 - 80, have low bone density (T scores less than -1.0). The population proportion of seniors between the age of 65 - 80 who have low bone density was 0.38 five years ago. To see if the proportion of seniors aged 65 - 80 who have low bone density has changed, 85 participants underwent bone density tests. a. Using the central limit theorem, what is the probability that the sample proportion is less than 0.365? b. Using the central limit theorem, what is the probability that the sample proportion is greater than 0.40?

5. It is believed that a greater proportion of Canadians own minivans compared to Americans. In a random sample of 500 Canadian households, 120 are found to own at least one minivan while in a random sample of 700 American households, 132 own minivans. (a) What is the null and research hypothesis? (b) What is the weighted average (or pooled proportion) of households who own minivans? (c) What is the standard error of the difference of two proportions for this problem? (d) following the results from above questions (a) and (b), what is the value of z? (e) If the significant level is 5% ( alpha = .05), what conclusion is reached about the null hypothesis Show some proof to support this conclusion.

6. A study is undertaken to test the emission levels of minivans. At the outset, a research hypothesis is established that states more than 75% of minivans meet emission standards (Null hypothesis is that 75% meet the standard). An alpha value of 0.05 is chosen. A sample of 180 minivans is then selected. Of these cars, 130 cars met the standard. What conclusion can be reached about the null hypothesis?