Problem: You are a researcher for the Columbus Restaurant Council. You are asked to get a representative sample of managers from all restaurants in the Columbus, Ohio area and survey them on health and safety measures used at their restaurant. The following sampling methods are proposed. Identify the sampling methods described.

1. The restaurants are separated into 3 size categories: small (under 30 seats), medium (31 to 80 seats), and large (more than 81 seats). A random sample of 20 small restaurants, 20 medium restaurants, and 20 large restaurants is selected
2. Eight zip codes in Columbus Ohio are randomly selected. All the restaurants in those zip codes are selected to be included in the sample.
3. Each member of the Columbus Restaurant Council volunteers their restaurant to be included in the sample.
4. A master list of all the restaurants in Columbus is created. Each is assigned a number. You use a program to generate 100 random numbers and choose the restaurants associated with those numbers to be in the sample.
5. The restaurants are classified according to the average price of an entrée: $, $$, $$$, $$$$. 10 restaurants are randomly selected from each price category to be in the sample.

1. The Columbus Restaurant Council has determined that the minimum amount a small-sized restaurant should spend annually on communicable disease prevention training is $3,850. This would allow for at least two employee training sessions from the local health department. Based on their survey of 88 small-sized restaurants, they found that the average amount spent on communicable disease prevention training is $3,829 with a standard deviation of $51.00. Test the hypothesis that small-sized restaurants are spending less than the required $3,850 annually. Use and alpha of .05 to conduct the test.
   1. Hypotheses:
      
   2. What is the critical value of the test statistic?
      
   3. What is the calculated value of the test statistic? (Show formula or calculator command)
      
   4. What is the p-value of the test statistic?
      
   5. State and support your decision about the null hypothesis.
   6. Construct a 95% confidence interval for the average amount small-sized restaurants are spending on communicable disease prevention training.
      
   7. What is your final conclusion about the amount small-sized restaurants are spending on communicable disease prevention training. Discuss the results of the hypothesis test in your answer.
      Giant Fish supermarket currently has hired you to do a survey of customers at the store so that they can have a better understanding of the customers shopping at their stores.
      The following data obtained from a simple random sample of 15 shoppers will be used to answer several questions.
      TABLE 1.

      Customer	Gender	Age	Number of Shopping trips (per month)	Amount Spent ($ per trip)
      1	F	32	9	92.00
      2	F	19	6	120.00
      3	F	48	14	79.00
      4	M	27	10	84.00
      5	F	66	6	144.00
      6	F	54	8	89.00
      7	M	38	12	68.00
      8	M	44	9	75.00
      9	F	37	6	106.00
      10	M	71	5	99.00
      11	F	25	9	87.00
      12	F	55	8	93.00
      13	M	61	7	102.00
      14	M	31	11	74.00
      15	F	42	8	93.00

2. (4) Given the data in Table 1, calculate 2 measures of central tendency (center) and 2 measures of variability for the "Amount Spent ($ per trip)" variable.

   Name of Measure of Center	Value of Measure of Center	Name of Measure of Variability	Value of Measure of Variability

   
   Note: Use T ABLE 1 to answer question 4.
3. The CEO of Giant Fish supermarket suspects that customers who shop more frequently tend to spend less on each shopping trip. To investigate this trend he would like you to conduct a simple linear regression using the number of Shopping Trips (per month) as the independent variable and the Amount Spent (per trip) as the dependent variable.

1. (2) Create the scatter plot and label the graph and both axes .
2. (4) Calculate the regression equation.
   ____________________________
3. (2) Sketch the regression equation line on the graph above.
4. (2) Determine the correlation coefficient ______________
   
   and the coefficient of determination ______________ and label each with the appropriate symbol.
5. (2) Describe the relationship (correlation) between the number of shopping trips per month and the amount spent per trip, using at least two descriptors.
   
6. (2) Use the regression equation to predict the amount spent per trip for:
   1. a person who goes to the store 7 times per month.______________
   2. a person who goes to the store 11 times per month.______________
7. (2) Which is greater, the predicted amount or the actual amount spent per trip, for a person (customer # 13) who goes to the store 7 times per month?
   ____________________________________________________________
8. (2) Why can't you predict the amount spent per trip for someone who goes to the store twice per month?

_____________________________________________________________

1. The owner of Giant Fish supermarket is considering conducting a study to try to correlate the average household income with the amount spent per shopping trip.
   1. (4) Determine the minimum sample size needed to estimate the average household income to within $2,000 of the true average income at the 95% confidence level. Prior studies have shown that the standard deviation in the population is $8,000.
   2. (4) Give two specific recommendations for the study that would sufficiently reduce the required size of the sample.
2. The owner of Giant Fish supermarket wants to know if the proportion of households who regularly shop at his store is the same on the east and west sides of Columbus. You survey 800 households on the east side of Columbus and find that 358 of them shop at Giant Fish regularly. You survey 600 households on the west side of Columbus and find that 289 of them shop at Giant Fist regularly. Conduct a test to determine if proportion of households who regularly patronize Giant Fish supermarket is the same on the east and west sides of Columbus. Use an alpha of .05 to conduct the test.
   Conduct (10) Show all 5 Steps of Hypothesis Testing and interpret your decision .
   (2) Hypotheses are:
   
   (4) The value of the test statistic is ____ _________ and the p-value is ____________
   (2)Decision:
   
   (2) Interpretation (in the words of the problem):
   
   B) (3) Construct a 95% confidence interval for the proportion of households who regularly shop at Giant Fish supermarket on the WEST side of Columbus.
   ________________________
   C) (3) Interpret this interval:
   N ote: Use Table 1 to answ er problem 7
3. The owner of Giant Fish supermarket is interested in the average of age of shoppers in the store. Create and interpret a 95% confidence interval for the average age of shoppers in the Giant Fish supermarket.

1. (2) Interval: _______________________
2. (2) Interpretation: __________________________________________
3. (2) What is the point estimate for the average age of shoppers at Giant Fish supermarket?
   ____________
4. (2) What is the margin of error?
   ____________
5. (2) The U.S. Supermarket Marketing Group reported that the average age of supermarket shoppers is 43.5 years. Are the ages of the shoppers at Giant Fish significantly different than the national average age?

N ote: Use Table 1 to answ er problem 8

1. The owner of Giant Fish supermarket believes that women spend significantly more at the grocery store than men.

1. (8) Test the hypothesis that there is no difference in the amount men and women spend at the supermarket. Assume that the two samples are independent and nearly normal. (Use α = .05)

Show all 5 steps of hypothesis testing and support your decision with a either a test statistic and critical value or p-value.

1. The owner of Giant Fish supermarket was looking at some data from a survey conducted in 2012. This survey analyzed the customer ratings of the restroom facilities at the supermarket. Based on the summary data below, determine if restroom ratings are independent of gender. Use an alpha of .05 to conduct the test and assume all respondents are independent.

   	Above Average	Average	Below Average
   Male	7	24	28
   Female	8	26	7

   1. (2) State the hypotheses being tested.
   2. (2) Complete the table of expected frequencies:
      

      	Above Average	Average	Below Average
      Male
      Female

   3. (2) Give the computed value of the test statistic:
      ____________________________
   4. (2) What is the p-value of the test?
      ____________________________
   5. (2) State and explain the decision
2. (9) The owner of Big Fish supermarket was reviewing some data from a research report on the type of advertisements in the local paper that are most effective. Three types of ads (big headline, straight forward and bold print) were randomly alternated over a period of weeks and the number of shoppers that reported that they read the ad was tallied. Do the data below support the hypothesis that there is no difference in the effectiveness of the ads, as measured by the mean number of shoppers who reported reading the ad? Use an alpha of .05.

   Type of Advertisement
   Big Headline	Straight Forward	Bold Print
   23	19	28
   42	31	33
   36	18	46
   48	24	29
   33	26	34
   26	25	34

   
   Conduct all steps of an ANOVA hypothesis test. Remember to include hypotheses, test statistic, p-value, and decision.) What is your conclusion? Explain what this means in context. Remember to use full sentences and correct grammar.
   
3. (9) The owner of Giant Fish supermarket has asked you to use a sample of 8 customers to determine if a television commercial affects the likelihood of purchasing a new brand of fish sauce. The customers selected rated the purchase potential of the new brand of sauce both before and after seeing a television commercial for the sauce. The customer ratings range from 0 to 10 with a higher value indicating a higher purchase potential. Test the hypothesis that the commercial significantly changed the ratings of the purchase potential of the fish sauce. Use an alpha of .05 to conduct the test.

12. (6) Write a summary of your results from all of the analyses above for the owner of Big Fish supermarket. Make sure to discuss the results from each of the questions 2-11 in the exam. This summary should be in the form of a paragraph, suitable for your intended audience, and should use full sentences and correct grammar.

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