**Question 2**The city of Chicago decides to understand whether its citizens consume more alcohol during the summer period. As a baseline, the average person consumes 0.7L of alcoholic beverages each week outside the summertime. In June of a given year, they collected a simple random survey of 28 people and estimated an average per capita consumption of 0.95L per week. Moreover, they estimated a sample variance of 0.85L².a) State the null and alternative hypothesis of the test.b) Compute the relevant test statistic. Show all steps.c) The researchers conducting this assessment decide to restrict the type 1 error to 10%. Find the critical value(s) for the test and justify your answer.d) Find the p-value for the test. Explain your answer. Draw a graph with a representation of the p-value with the relevant values in the test.e) Conclude the test.

The question is about hypo. testing Given : Popl. avg. of alcoholic beverages that person consumes per week ( μ ) = 0.7 L Randomly selected no. of people ( n ) = 28 Sample mean per capita alcohol consumption per week ( x¯ ) = 0.95 L Sample var. of per capita alcohol consumption per week ( s2 ) = 0.85 L2 To find : Test whether the citizens consumes more alcohol during summer perioda ) Null and alt. hypo : H0 : μ = 0.7Ha : μ > 0.7 b ) As popl. std. deviation is unknown and sample var. is known hence t test must be used The formula of test stat is given by t = x¯ - μs2n = 0.95 - 0.70.8528 = 0.250.174233t = 1.43486 c ) Given : type I error ( α ) = 10 % = 0.10 As alt. hypo. has > sign, so it is right tailed test df = n - 1 = 28 - 1 = 27 tcritical = t1-α,df = t1-0.10,27 = t0.9,27 Critical value can be find by using excel command, =T.INV ( prob., df ) So, tcritical = 1.313703 d ) Shaded area indicates p value p value can be find by using excel command, =T.DIST.RT ( Test stat, df ) So, p value = 0.081405 e ) Decision rule : If p value < level of signif. ( α ) then reject H0 otherwise fail to reject H0 Here, p value < α Hence, reject H0 Conclusion : There is suffi. evid. to conclude that the citizens consumes more alcohol during summer period