Please answer and explain + show work

1.4.5 Suppose you are testing the hypothesis H0: 1: = 0.50 versus Ha: Jr > 0.50. You get a sample proportion of 0.54 and nd that your p-value is 0.08. Now suppose you redid your study with each of the following changes. Will your new p-value be larger or smaller than the 0.08 your rst obtained? a. You increase the sample size and still nd a sample pro- portion of 0.54. . Keeping the sample size the same. you take a new sample and nd a sample proportion of 0.55. . With your original sample, you decided to test a two- sided alternative instead of Ha: If > 050. Right or left 1.3.13 Most people are right-handed, and even the right eye is dominant for most people. Molecular biologists have suggested that late-stage human embryos tend to turn their heads to the right. In a study reported in Nature (2003). German biorpsychologist Onur Giintiirkn conjectured that this tendency to turn to the right manifests itself in other ways as well, so he studied kissing couples to see which side they tended to lean their heads while kissing. He and his researchers observed kissing couples in public places such as airports. train stations, beaches. and parks. They were careful not to include couples who were holding objects such as luggage that might have affected which di- rection they turned. For each kissing couple observed. the researchers noted whether the couple leaned their heads to the right or to the left. 'lhey observed [24 couples, age 1370 years. Suppose that we want to use the data from this study to investigate whether kissing couples tend to lean their heads right more often than would happen by random chance. . Dene the parameter of interest in the context of the study and assign a symbol to it. . State the null hypothesis and the alternative hypothesis using the symbol dened in part (a). . Of the 124 kissing couples, 80 were observed to lean their heads right. What is the observed proportion of kissing couples who leaned their heads to the right? What sym- bol should you use to represent this value? . Determine the standardized statistic from the data. (Hint: You will need to get the standard deviation of the simu- lated statistics from the null distribution.) . Interpret the standardized statistic in the context of the study. (Hint: You need to talk about the value of your ob- served statistic in terms of standard deviations assuming is true.) Based on the standardized statistic, state the conclusion that you would draw about the null and alternative hypotheses