Can L-lysine, an over the counter vitamin, help reduce the number of cold sores a person experiences, on average? A random sample of 32 adults were asked to record the number of cold sores they experienced over a one-year period (without L-lysine), then the same adults were asked to record the number of cold sores they experienced during the following one-year period while taking L-lysine once per day as instructed. 4.a The researchers wished to assess whether the number of cold sores experienced was reduced, on average, while taking L-lysine. A 5% significance level will be used. Let the parameter d represent the population mean difference in the number of cold sores experienced in a one-year period (Non L-lysine less L-lysine, that is d = non Llysine count minus L-lysine) for the population of all people. The researcher knows that the null hypothesis of no difference on average should be expressed as H0: d = 0. Which direction is the appropriate one to correctly complete the alternative hypothesis Ha: d __ 0? greater than (>) less than (<) not equal to 4.b You remember that the next step after formulating hypotheses and selecting the significance level, is to state and check the assumptions/conditions. You remember that one of the assumptions has something to do with randomness. Which of the following is that appropriate assumption? The two populations,non L-lysine users and L-lysine users, are random. The two samples, non L-lysine users and L-lysine users, are randomly selected from the two populations. The population of all differences in cold sore count measurements is random. The sample of differences in cold sore count measurements is randomly selected from the population of all possible differences. The two populations, non L-lysine users and L-lysine users, are independent from each other. The two samples, non L-lysine users and L-lysine users, are independent from each other. 4.c You also remember that the other assumption to be checked has something to do with normality. Which one of the following is the best, most precise statement of that remaining assumption? The underlying population of all L-lysine users is normally distributed. The underlying population of all non L-lysine users is normally distributed. The population of differences in non L-lysine users minus L-lysine users for all people is normally distributed. The population of differences in the number of cold sores (non L-lysine minus L-lysine) for all people is normally distributed. The sample of differences in the number of cold sores (non L-lysine minus L-lysine) for the 32 subjects is normally distributed. The underlying population of the number of cold sores in a year for all people is normally distributed. The sample of the number of cold sores for the 32 subjects is normally distributed. 4.d To check the normality assumption, we must make (an) appropriate plot(s). Which of the following is appropriate for our scenario? Plot A is given below: Plot B is given below: Plot C is given below: Plot A only Plot B only Plot C only Plots A and B Plots A, B, and C 4.e The assumption regarding normality does not appear to be met based on the graph(s) in part d. Why are we able to still proceed and perform the corresponding paired t-test? The Central Limit Theorem states that any sample size will allow the t-test to proceed anyway. Because the sample size is at least 10, we may proceed with the t-test anyway because of the Central Limit Theorem. Because the sample size is at least 25, we may proceed with the t-test anyway because of the Central Limit Theorem. Because I have 64 observations (32 measurements for non L-lysine and 32 measurements for Llysine), which is at least 25, we may proceed with the t-test anyway because of the Central Limit Theorem. 4.f If we were asked to provide a 95% confidence interval to estimate the population mean difference in cold sores in a year (non L-lysine minus L-lysine), which of the following R outputs would give us that appropriate confidence interval? Paired t-test data: NonLysine and Lysine t = 8.784, df = 31, p-value = **** alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: 1.463645 2.348855 sample estimates: mean of the differences 1.90625 Paired t-test data: NonLysine and Lysine t = 8.784, df = 31, p-value = **** alternative hypothesis: true difference in means is less than 0 95 percent confidence interval: -Inf 2.274203 sample estimates: mean of the differences 1.90625 Paired t-test data: NonLysine and Lysine t = 8.784, df = 31, p-value = **** alternative hypothesis: true difference in means is greater than 0 95 percent confidence interval: 1.538297 Inf sample estimates: mean of the differences 1.90625 4.g Here are some additional summary measures of the variables associated with the number of cold sores. Which of the following values from this summary output correctly completes this interpretation statement? We would estimate the possible sample mean differences in the number of cold sores (d d values) to be about ______ cold sores away from the population mean difference in the number of cold sores d, on average. 1.2276223 0.2170150 0.1730850 0.2219666 4.h What distribution is used to find the p-value for the test? standard normal N(0,1) distribution a t(31) distribution a t(32) distribution 4.i 1 point(s) Because the p-value is very small, nearly 0, what will be our decision at the 5% level and the conclusion in context? At 5% significance level, reject the null hypothesis and conclude that there is insufficient evidence to suggest that taking L-lysine daily will reduce the number of cold sores experienced in a one-year period, on average. At 5% significance level, reject the null hypothesis and conclude that there is sufficient evidence to suggest that taking L-lysine daily will reduce the number of cold sores experienced in a oneyear period, on average. At 5% significance level, fail to reject the null hypothesis and conclude that there is sufficient evidence to suggest that taking L-lysine daily will reduce the number of cold sores experienced in a one-year period, on average. At 5% significance level, fail to reject the null hypothesis and conclude that there is insufficient evidence to suggest that taking L-lysine daily will reduce the number of cold sores experienced in a one-year period, on average