Your friend owns a retail store where she plans to give arrivingcustomers a short verbal ”commercial” message regarding productsfor sale. Your friend asks you to determine if this will boost theaverage dollar value of sales to each customer, µ, which iscurrently $5.00. You may assume that the standard deviation pertransaction is $1.00 and that the population is of unlimited size.You monitor a random sample of n = 200 customers given the shortverbal ”commercial” message upon arrival at the store and determinethe amount purchased by each. (a) Your friend will only adopt thepolicy of giving short verbal ”commercial” messages to each newlyarriving customer if the sample indicates that the values of salesper customer will improve. Formulate the null and alternativehypotheses. [2 marks] (b) Suppose you wish to test the nullhypothesis while ensuring that your friend only has a 5% chance ofgetting a recommendation to adopt the policy of giving short verbal”commercial” messages when that policy actually does not improvethe value of sales per customer. Describe the test statistic youwould use to conduct the test, compute the critical region for thetest, and describe the decision rule you would use. [4 marks] (c)You collect the sample data. What recommendation would you make toyour friend if (i) X¯=$5.37, (ii) X¯=$5.05, (iii) X¯=$4.97, and(iv) X¯=$5.20 ? Express your recommendations as formal hypothesistesting conclusions. [4 marks]