Question 4 (13 marks) Pure breed peas were crossed to produce smooth and wrinkled peas. The rst-generation peas were all smooth. In the second generation, 5474 smooth and 1850 wrinkled peas were obtained. Do the data agree with the conclusion of 75% dominant trait (here "smooth\"] occurrence in the second generation? a] Find a point estimate for a proportion of smooth peas. b) Use the plus four method to construct a 95% condence interval for a proportion of smooth peas using the standard normal distribution. State your conclusion. c) Perform a test using a Chi-square distribution at a signicance level of 0.05. Question 5 (15 marks) To test for a relationship between gender and souvenir shopping, a survey of more than 3,000 tourists was conducted. One question asked how often a tourist purchases photographs, postcards, or paintings of the region visited. Responses were recorded as \"always , often , occasionally\Question 1 (14 marks) To combat red-light-running crashes (the phenomenon of a motorist entering an intersection after the traffic signal turns red and causing a crash), many states are adopting photo-red enforcement programs. In these programs, red light cameras installed at dangerous intersections photograph the license plates of vehicles that run the red light. The following table displays the number of crashes per year for 5 intersections in Virginia both before and after installation of red light cameras. Intersection Before camera After camera 3.6 1.3 2 0.2 0 0.3 0 4 4.5 1.7 5 2.6 2.0 Are photo-red enforcement programs effective in reducing red-light-running crash incidents at intersection? a) Construct a suitable confidence interval at a confidence level of 90%. State your conclusion. b) Perform a suitable test at a significance level of 0.05. c) Is the conclusion from the confidence interval calculation above the same as the conclusion of the test above? Explain why or why not. Question 2 (14 marks) A British statistician and biologist introduced a data set which consists of 50 samples from each of two species of Iris (Iris setosa and Iris versicolor). The width of sepals was measured from each sample in centimetres. This data set is available as Excel file "sepal width.xlsx" on Moodle in the "Assessment" block. Does the data provide evidence for a difference in the sepal widths between Iris setosa and Iris versicolor? a) Construct a suitable confidence interval at a confidence level of 95%. State your conclusion. b) Conduct a suitable test of significance at a significance level of 5%. c) Is the conclusion from the confidence interval calculation above the same as the conclusion of the test above? Explain why or why not. Question 3 (8 marks) Consumer Reports evaluated and rated 24 brands of toothpaste. One attribute examined in the study was whether or not a toothpaste brand carries an American Dental Association (ADA) seal verifying effective decay prevention. The data for the brands (coded 1=ADA seal, 0=no ADA seal) are listed here. 1 0 0 0 1 0 0 1 0 0 1 1 1 0 0 1 0 1 1 1 Perform a suitable test at a significance level of 5% if a majority of toothpaste brands carries the ADA seal. of 2