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Part A [12 marks in total] A recent study reported that New Zealand smart phone subscribers averaged 4.3 hours per week watching videos on their smart phones. A film studies lecturer wanted to do a hypothesis test to find out if this average is true for New Zealand university students or not. She asked all the students in her large first year film studies class at Massey University how many hours they spent watching videos on their smart phones during the previous week. 50 students responded. Summary statistics (in hours per week) for the data are: Sample mean = 6.99 Sample standard deviation = 3.35 Standard error = 0.4742 Part A continues on next page… Part B [11 marks in total] Researchers were interested in the effect of flower colour on insect pollination. They counted the number of insects from three different species (Beetles, Flies and Bees/Wasps) that visited white, yellow and blue flowers during a 24hour period. The table and graph below summarise their results. RStudio was used to do a Chi-squared test on this data. The RStudio output for the test, the expected counts and the residuals are below. Part B continues on next page… Part B continues on next page… Part C [11 Questions worth 16 marks in total] A statistics student wanted to see if there is a relationship between the calories and alcohol content of beer. He recorded the calories (per 360ml) and alcohol content (percentage) for the first 85 beers listed on the webpage of a local supermarket. The data is shown in the scatterplot below. The correlation coefficient is also shown below. RStudio was used to fit a linear model to the data. Below are the RStudio output, the residual plot and a histogram of the residuals. Part C continues on next page… Part C continues on next page… Part D[6 Questions worth 12 marks in total] A study was carried out looking for links between diet and development of Alzheimers disease. 341 elderly people participated. For six years researchers tracked what these participants ate and drank, and monitored who went on to develop Alzheimers. The participants were subsequently divided into two groups based on the amount of tea they drank each day. The group that drank 3 or more cups of tea daily were called Group A. The other group drank less than 3 cups of tea per day were called Group B. The results are summarised in the plots below: A two-sample hypothesis test of proportions was carried out. Below are the hypotheses for this test. The null: There is no difference between the proportion with Alzheimers in the two groups. The alternative: There is a difference between the proportion with Alzheimers in the two groups. The test gave a p-value of 0.001181. The 95% confidence interval for the difference between proportions (Group B Group A) has a lower limit of 0.0568 and an upper limit of 0.236. Part D continues on next page…. + + + + + + +

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