Samantha has over 500 songs on her mobile phone, and she wants to estimate the proportion of the songs that are by female artists. She takes a random sample of 50 songs on her phone and finds that 17 of these songs are by a female artist. Based on this information, complete the following questions, a) Show that the requirements to build a confidence interval are met. b) State the critical value for an 85% confidence interval c) Compute the 85% confidence interval. State values to two decimal places. d) Interpret the 85% confidence interval using complete sentences. * This is a confidare intend for a singe propustian since we must estimate the propation of songs by favok anny's a) Requiremnants * ST2S (simpto vandem comple) given No1 valu cho ni-t) > 10 (1.3461-0.24) 11.22 . 'Va=0.344 hs 50 b) Critical value 1 -0.85 = 0.5 0.15/2 = 0.675 vialt talata; lock invejck Thy z teslok fu the left tail area to determine the arrical value 2' =1.44 c) Carlida ke Internal P=0.34 0.34(1-0.31) = 0.007 = 2-F 50 0.34 +1.44(0.067) (0.24, 0.44) d) Interpretation we are 85% Carricknt the presion of phans that art ly fernal ands is between 0.24 and 0.44. songs on the malac Math 146 Purpose In this assignment you will practice building and interpreting confidence intervals. Confidence intervals are used to give a range of plausible values for the population mean or proportion under consideration. If you have ever read the results of a poll, you might recall that a percentage is given followed by the statement, ...plus or minus...\" some value. For example, the presidential approval rating is 49% plus or minus 1.73%. The 49% is the sample proportion with the 1.73% noting the margin of error Understanding how confidence intervals are built and interpreted will help you become a better consumer of information. Confidence intervals are used in a variety of applications besides analyzing polling data. For instance, manufacturing clothing (sizes are based on an average plus or minus an acceptable error), volume of food items (the 12oz cereal box holds on average 12oz plus or minus a margin of error), lifetimes of items (a lightbulb will last on average 400 hours plus or minus a n acceptable error), etc. Task Based on USDA suggestion, a U.S. adult should be spending anywhere from $165 to $345 per month on food, depending on age and gender. A random sample of 120 adults in Washington State is polled regarding the amount of money they spend each month on food. The sample has an average of $273.61 with a standard deviation of $61.59. Based on this information, complete the following questions. a) (spts)Show that the requirements to build a confidence interval are met. b) (spts) State the critical value for a 90% confidence interval c) (Spts)Compute the 90% confidence interval. State values to two decimal places. d) (spts)Interpret the 90% confidence interval using complete sentences. Criteria for Success You should imagine that you are writing up this solution as you would on an exam. State answers clearly with proper notation. The example in the other link provided in this assignment illustrates the desired work, proper notation and explanations. Pay close attention to the wording of the confidence interval interpretation