Please provide full equations and explanations. For confidence intervals use the equation ( sample estimate + or - CV times SE). Use the formulas to get the critical value and standard error. Use formulas for to find ( T *). Find the intervals from population mean using ( X mean + or - T* times Standard deviation square root of N). Thank you!

In a 2023 survey of 4,323 adults living in the U.S., it was found that 14% identified the environment being the issue that mattered the most to them at the moment. [77] 1) Construct a 95% confidence interval for the proportion of adults living in the U.S. that would identify the environment being the issue that matters the most to them at the moment. 2) Interpret the interval in part a Veldhuis, Alleva, and Big devata [72] conducted a study where the purpose was to investigate the relationship between body image, self-objectification, self-esteem, and various selfie behaviors among young women. The study included 179 women between the ages of 18-25 who reported taking selfies. A key interest was in the number of weekly selfies posted. Of the participants, the average number of selfies posted per week was 1.56 with a standard deviation of 3.4. 1) Construct a 95% confidence interval for the average number of selfies posted per week. 2) Interpret the interval in part a. 3) From the interval, can we conclude that the average number of selfies posted per week is more than 1? Swinkels, Newman, and Allain (2008) investigated falls among elderly patients that will be getting a knee replacement. [65] Patients were classified as either "fallers" or "non-fallers". One of the items investigated was their pain level on a scale from 0-20 where 20 is the worst. For the 75 pre-operative non-fallers. their mean pain score was 10.4 with a standard deviation of 3.3. For the 24 pre-operative fallers, their mean pain score was 11.7 with a standard deviation of 2.7. 1) Calculate a 95% confidence interval for the difference between the mean pain score for pre-operative non-fallers and pre-operative fallers. Note that the pooled variance is 10.036. 2) Interpret the interval in part a. 3) From the interval, can we conclude a difference between the mean pain score of pre-operative non-fallers and pre-operative fallers? If yes, which is higher Search