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. [4 marks] 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 estimated that 22% of adults living in Canada have an IQ score greater than 115. Researchers are interested if the proportion of adults in a certain city that contains a University and a College is greater than the Canadian average. 361 adults had their IQ's tested, and it was found that 93 had an IQ greater than 115.

do a 95% confidence interval for the proportion of adults who have IQ's greater than 115 in the city. Is it reasonable to assume that the proportion of adults in the city whose IQ is greater than 115 is higher than the Canadian average of 22%? [10 marks] a. What is the null and alternative hypothesis for the proportion testing? b. What is the significant level to analyze the test? c. Is it a two-tailed test or one-tailed test? d. what is the critical value of the testing? e. what is the sample proportion value? f. What is the standard error of proportions? g. What kind of test statistic formular is being used and what is the particular value here? h. What is the decision rule to test the hypothesis? i. What are your conclusions?

6. In 2020, the mean weight of men ages 25 - 40 in a certain Canadian city was normally distributed with a mean of 226 lbs and a population standard deviation of 28.5 lbs. A research study is being conducted to see if the average weight of men ages 25 - 40 in the city has changed since 2020. A sample of 45 men aged 25 - 40 revealed a mean weight of 231 lbs. At the 0.05 level of significance, can we say that the mean weight has changed since 2020? Please use the statistics testing method to analyze the questions and draw your conclusions. [5 marks]