1 Problem 4: Monday Night Deals In an attempt to increase business on Monday nights, a restaurant offers a free dessert with every dinner order. Before the offer, the mean number of dinner customers on Monday was 150. The numbers of diners on a random sample of 12 days while the offer was in effect are selected. Can you conclude that the mean number of diners increased while the free dessert offer was in effect? a) What is (are) the parameter(s) we are conducting inference on? Choose one of the following symbols ( D (the mean difference from a matched pairs design) 2 (the mean difference from independent samples) and describe it in words. b) Construct a histogram and a boxplot to visualize the distribution of your sample data. Copy and paste these graphs into your assignment. Below the graphs, answer the following questions. i. Are there any major deviations from normality? ii. Are there any outliers present? iii. Is it appropriate to conduct statistical inference procedures, why or why not? If the answer to part iii is no, do not complete the rest of #4. c) At the 0.10 significance level, can you conclude that the mean number of diners increased from 150 while the free dessert offer was in effect? i. State the null and alternative hypotheses. ii. State the significance level for this problem. iii. Calculate the test statistic. iv. Calculate the P-value and include the probability notation statement. v. State whether you reject or do not reject the null hypothesis. vi. State your conclusion in context of the problem (i.e. interpret your results). d) Construct a 90% confidence interval for the above data. Interpret the confidence interval