Directions: Answer the following questions and solving the following problems for the following context.After medically-supervised obese adults leave a six-month in-patient treatment program of diet and exercise to foster healthy weight loss, these patients are monitored as they transition back into their own homes. Clinical dieticians are curious if there is significant additional weight loss during the next month of home care. A random sample of 16 adults includes the following data, in pounds, which measures their weights immediately upon leaving the in-patient program (pre-test) and again after one month of home maintenance of the weight loss program (post-test). Pre-Test315280350300420380225360Post-Test295285335320400350225340 Pre-Test295360240305310255300360Post-Test280345245320300250305360 At the 5% level of significance, test the claim. [COMMENTS & HINTS: Utilize the test sheet and keep it handy when answering these questions. Note that this is one collection of matched pair data, with 16 pairs. QUESTION 19As a reminder, what is the level of significance in this statistical analysis?Express the answer as a whole percentage with percent symbol.QUESTION 20How does the p-value compare against the level of significance, a, under the corresponding tail of the probability distribution?The p-value is less than or does not exceed the level of significance, (a).The p-value is greater than or exceeds the level of significance, (x).The p-value is equal to the level of significance, (a).It cannot be determined at this time if the p-value is less than, greater than or equal to the level of significance, (a)QUESTION 21What is the technical conclusion to this hypothesis testing?Reject the null hypothesis based on the available evidence (matched pair samples of size 16) and testing at the 5% level of significance.Marginally reject the null hypothesis based on the available evidence (matched pair samples of size 16) and testing at the 5% level of significance.Highly reject the null hypothesis based on the available evidence (matched pair samples of size 16) and testing at the 5% level of significance.Fail to reject the null hypothesis based on the available evidence (matched pair samples of size 16) and testing at the 5% level of significance.Marginally fail to reject the null hypothesis based on the available evidence (matched pair samples of size 16) and testing at the 5% level of significance.O Highly fail to reject the null hypothesis based on the available evidence (matched pair samples of size of 16) and testing at the 5% level of significance.QUESTION 22What is the contextual conclusion to this hypothesis testing?It is unreasonable to claim that there is no difference in mean weights from pre-test to post-test, based on the available evidence (matched pair samples of size 16) and testing at the 5% level of significance.It is marginally unreasonable to claim that there is no difference in mean weights from pre-test to post-test, based on the available evidence (matched pair samples of size 16) and testing at the 5% level of significance.It is highly unreasonable to claim that there is no difference in mean weights from pre-test to post-test, based on the available evidence (matched pair samples of size 16) and testing at the 5% level of significance.It is reasonable to claim that there is no difference in mean weights from pre-test to post-test, based on the available evidence (matched pair samples of size 16) and testing at the 5% level of significance.It is marginally reasonable to claim that there is no difference in mean weights from pre-test to post-test, based on the available evidence (matched pair samples of size 16) and testing at the 5% level of significance.It is highly reasonable to claim that the mean amount of food purchased is $200, based on the available evidence (sample size of 64) and testing at the 5% level of significance.QUESTION 23How statistically interesting is this finding?It is statistically insignificant and uninteresting.It is marginally statistically insignificant and uninteresting.It is highly statistically insignificant and uninteresting.It is statistically significant and interesting.It is marginally statistically significant and interesting.It is highly statistically significant and interesting.O O O

Null Hypothesis: A hypothesis which is tested for plausible rejection is called the Null Hypothesis (typically denoted by H0). Alternative Hypothesis: Any hypothesis contradicting null hypothesis is called Alternative Hypothesis (typically denoted by H1). Critical Value: In test of hypotheses, Critical Values are the cut-off values that provide with the regions in which the test statistic is unlikely to lie. Level of Significance: In testing of hypothesis, Level of Significance is the probability of rejecting a null hypothesis when it is true. In other words, if the value of test statistic exceeds the critical value, we conclude that the null hypothesis has been rejected. Test Statistic: In statistical hypothesis testing, a test statistic is a number calculated from the values of the sample or if any value(s) from the population has been provided. It shows how closely the observed data match the distribution expected under the null hypothesis of that statistical test. p-value: In testing of hypothesis, the p-value represents the probability of getting results at least as extreme as the observed results of the test, under the assumption that the null hypothesis is true.Let us assume x and y be the pre-test and post-test weights of a randomly selected adult respectively. Since, both weights were measured on the same individual then, we have x and y are distributed in Bivariate Normal form with mean μx and μy, standard deviations σx and σy and correlation coefficient ρ. Here we want to test if there is significant additional weight loss during the next month of home care. So, our null hypothesis to test is: against the alternative hypothesis For this, we define a new variable d = x - y. Therefore, This provides us with a new equivalent set of hypotheses, against We will perform Paired t-test. The test statistic to test H0 is, which follows t-distribution with degrees of freedom (n - 1) under H0. where, n is number of observations, being the sample mean of x and y respectively, sd' is the sample standard deviation of d with divisor (n - 1). From the t-value, we calculate p-value for this test using MS-Excel, We reject H0 at α significance level if and accept otherwise. Here, we have From the 16 pair scores, we calculate Therefore, the value of the test statistic is, From the t-value, we calculate p-value for this test using MS-Excel, We are given Clearly, Therefore, we accept H0 at 5% level of significance. Conclusion: At 5% level of significance, there is not enough evidence to support the claim that there is significant additional weight loss during the next month of home care. Solution 19: The blank will be filled up with 5%. Solution 20: The correct answer is: Second Option. Solution 21: The correct answer is: Fourth Option. Solution 22: The correct answer is: Fourth Option. Solution 23: The correct answer is: First Option. (Answer)