1'1 WI HypOIHESIS tesung 6L sampling [llSII'lDLllIIOIlS 4. Body mass index (BMI) is a number calculated from a person's weight and height. In 2021 the (BMI) for adult males in the USA was 14 = 26.6 with a standard deviation 6 = 7.30. You are interested in testing a new fad diet and want to see if it will affect weight loss. You recruit a sample of n = 30 men who follow the diet guidelines for 4 weeks and afterwards their average BM] is 24.6. a. b. State the research hypothesis in words. State the research hypothesis in notation. State the null hypothesis in words. State the null hypothesis in notation. Calculate the standard error. Determine the critical values that indicate the points beyond which we will rej eet the null hypothesis. In this case, you should determine this assuming we have a 2-tailed test ( e.g., non-directional hypothesis) with a .05 cut-off. Calculate the Z score for your sample mean. Do you reject or fail to reject the null hypothesis? Provide the rationale for your answer above here. 5. Now let's say you recruit a sample of n = 90 men who follow the diet guidelines for 4 weeks and aerwards their average BMI is 24.6 a. b. Calculate the new standard error. Determine the critical values that indicate the points beyond which we will reject the null hypothesis. In this case, you should determine this assuming we have a 2-tailed test ( e.g., non-directional hypothesis) with a .05 cut-off. Calculate the Z score for your sample mean. Do you reject or fail to reject the null hypothesis? Provide the rationale for your answer above here. Did the results of your test change? Why? Make sure your answer includes information regarding the sample size and standard error