Parameters and hypotheses For each of the followingsituations, define the parameter (proportion or mean) and write the null and alternative hypotheses in terms of param-eter values. Example: We want to know if the proportion of up days in the stock market is 50%. Answer: Let p = theproportion of up days. Ho: p = 0.5 vs. HA: p ≠ 0.5.a) A casino wants to know if their slot machine reallydelivers the 1 in 100 win rate that it claims.b) A pharmaceutical company wonders if their new drughas a cure rate different from the 30% reported by theplacebo.c) A bank wants to know if the percentage of customersusing their website has changed from the 40% thatused it before their system crashed last week.

A survey was conducted to determine whether hours of sleep per night are independent of age. A sample of individuals was asked to indicate the number of hours of sleep per night with categorical options: fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more. Later in the survey, the individuals were asked to indicate their age with categorical options: age 39 or younger and age 40 or older. Sample data follow. Age Group Hours of Sleep 39 or younger 40 or older Fewer than 6 38 36 6 to 6.9 60 57 7 to 7.9 76 74 8 or more 66 93 (a) Conduct a test of independence to determine whether hours of sleep are independent of age. (b) What is your estimate of the percentages of individuals who sleep fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more per night?

Aspirin III: Decision and Conclusion Regarding the experiment in the data frame Aspirin from the abd package, the researchers wanted to know whether or not taking aspirin affects one's risk of developing cancer. Recall that they defined their parameters as follows: p1 = the proportion of ALL individuals who would develop cancer, if all of them were to take aspirin like the subjects in the Aspirin group did. p2 = the proportion of ALL individuals who would develop cancer, if all of them were to take a placebo, like the subjects in the placebo group did. They ran the code for a two-sided significance test and got the following results: ## ## ## Inferential Procedures for the Difference of Two Proportions p1-p2:##   cancer grouped by treatment ## ## ## Descriptive Results:## ##          yes     n estimated.prop## Aspirin 1438 19934        0.07214## Placebo 1427 19942        0.07156## ## ## Inferential Results:## ## Estimate of p1-p2:    0.0005805 ## SE(p1.hat - p2.hat):  0.002586 ## ##…

The Open Syllabus Project What statistical analysis could be used to determine of the mean percentage of psychology readings assigned in the Midwest was significantly different than in all of the United States?  Single-sample t-test In which of the following four categories does this situation fall? a. only scale variables b. nominal independent variables, scale dependent variable c. only nominal variables d. any ordinal variables (that cannot be treated as a nominal)