Q 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) (5pts)Show that the requirements to build a confidence interval are met. b) (5pts)State the critical value for a 90% confidence intervalc) (5pts)Compute the 90% confidence interval. State values to two decimal places.