Health Inspections of Restaurants

The New York City Department of Health and Mental Hygiene conducts regular inspections of restaurants.Each restaurant receives an inspection score, with lower scores indicating a more satisfactory inspection.Following are scores for the most recent inspection, as of October 2010, for random samples of 25 restaurants in the boroughs of Manhattan and Queens.Assume that the samples come from populations that are approximately normal.

Manhattan

2,22,23,0,40, 12, 37, 43,27, 15,24,8,38,4,17,21,11,18,13,30,27, 19,38,21 and4

Queens

27,18,14,20,35,8,42,29,0,12,25,0, 19,6,13,22,5,11,0,10,19, 39,2,8and 19

5.Draw appropriate graphs for each data set (boxplots are recommended).Include a graph comparing the means and standard deviations of the two data sets.Use EXCEL to generate these graphs.

6.Write a paragraph describing the similarities and differences between the two data sets, using appropriate descriptive statistics such as means, median, standard deviation, etc.

7.Perform a hypothesis test to determine whether the mean scores differ between the two boroughs? Use and let:

u1=mean inspection scores for restaurants in Manhattan

u2=mean inspection scores for restaurants in Queens

To perform the hypothesis test use the 5-step process:

a)State Ho and H1 in symbols and in words.Identify which hypothesis is the claim and the type of test (right-tail, left-tail, two tail).

b)Determine the critical value and label it. (example, z = 1.96or t = -2.421, etc).

c)Compute the test value, z or t.If you are using the p-value method, then compute the test value and include the p-value of the test (4 decimal places).

d)Make the decision toReject HoorDo not reject Ho.

e)State your complete conclusion in the context of the claim.

8. Discuss how this information and data might be used in the real world.