The article https://supchina.com/2018/04/02/kuora-why-northern-chinese-people-are- taller-than-southern-chinese/ argues that people from northern china are taller than people from southern China. The average height of 18-year-old males in China was 1.72 meters in 2014, and the average height of females was 1.60 m in 2014. Thus the average height of 18-year-olds in China was around 1.65 m. The dataset HKgrowthSamp.csv contains a sample of heights, weights, and BMIs of 100 people from a synthetic population of 25,000 18-year-olds in Hong Kong (see full dataset in Lab 6). Reading this article, one may deduce that people from Hong Kong should be shorter than people from mainland China. Let be the population mean height of 18-year-olds in Hong Kong and be its sample estimate. Does the data support the hypothesis that the population represented by this sample has a mean height less than 165 cm? (Hint: see Lab 6 for help with this question) a. Write out the null and alternative hypotheses, in terms of , for testing if the height of 18-year-olds in Hong Kong is less than 165 cm. Use a one-sided alternative hypothesis. b. Perform a one-sample t-test and report the p-value for testing if the sample mean height is less than 165 cm. Report the sample estimate for the sample mean height. c. Interpret the statistical results of the test. d. Give your scientific conclusions about the whether the data supports the hypothesis that the population represented by this sample has a mean height less than 165 cm. e. Imagine the researchers had specified a two-sided alternative hypothesis. Repeat part a. using a two-sided alternative hypothesis. f. Imagine the researchers had specified a two-sided alternative hypothesis. Repeat part b. using a two-sided alternative hypothesis. g. Imagine the researchers had specified a two-sided alternative hypothesis. Repeat part c. using a two-sided alternative hypothesis. h. Imagine the researchers had specified a two-sided alternative hypothesis. Repeat part d. using a two-sided alternative hypothesis.

i. In practice, researchers must think carefully about their scientific question to determine which hypothesis they want to test, and choose either a one-sided or two- sided test in advance. Discuss how your conclusions differ for a one-sided versus a two-sided test in this example. If you had been advising the researchers about which alternative hypothesis to select a priori, what would you have recommended?