The makers of Mini-Oats Cereal have an automated packaging machine that can be set at any targeted ...

The makers of Mini-Oats Cereal have an automated packaging machine that can be set at any targeted fill level between 12 and 32 ounces.
 
  Every box of cereal is not expected to contain exactly the targeted weight, but the average of all boxes filled should. At the end of every shift (eight hours), 16 boxes are selected at random and the mean and standard deviation of the sample are computed. Based on these sample results, the production control manager determines whether the filling machine needs to be readjusted or whether it remains all right to operate. Use  = 0.05. Establish the appropriate null and alternative hypotheses to be tested for boxes that are supposed to have an average of 24 ounces.A) H0 :  = 32 ounces Ha :   32 ounces
  B) H0 :  = 16 ounces Ha :   16 ounces
  C) H0 :  = 22 ounces Ha :   22 ounces
  D) H0 :  = 24 ounces Ha :   24 ounces

Q. 2

Applebee's International, Inc, is a U.S. company that develops, franchises, and operates the Applebee's Neighborhood Grill and Bar restaurant chain.
 
  It is the largest chain of casual dining restaurants in the country, with over 1,500 restaurants across the United States. The headquarters is located in Overland Park, Kansas. The company is interested in determining if mean weekly revenue differs among three restaurants in a particular city. The file entitled Applebees contains revenue data for a sample of weeks for each of the three locations.Test to determine if blocking the week on which the testing was done was necessary. Use a significance level of 0.05.A) The p-value = 0.078 >  = 0.05. This indicates that inserting the week on which the testing was done was necessary.
  B) The p-value = 0.078 >  = 0.05. This indicates that inserting the week on which the testing was done was not necessary.
  C) The p-value = 0.000 <  = 0.05. This indicates that inserting the week on which the testing was done was necessary.
  D) The p-value = 0.000 <  = 0.05. This indicates that inserting the week on which the testing was done was not necessary.

Q. 3

The roll of a pair of dice has the following probability distribution, where the random variable is the sum of the values produced by each die:
 
  x P(x)
  2 1/36
  3 2/36
  4 3/36
  5 4/36
  6 5/36
  7 6/36
  8 5/36
  9 4/36
  10 3/36
  11 2/36
  12 1/36
 
  Calculate the expected value of x.
  A) 6
  B) 7
  C) 8
  D) 9

Q. 4

Because of bad weather, the number of days next week that the captain of a charter fishing boat can leave port is uncertain. Let x = number of days that the boat is able to leave port per week.
 
  The following probability distribution for the variable, x, was determined based on historical data when the weather was poor:x P(x)0 0.051 0.102 0.103 0.204 0.205 0.156 0.157 0.05Based on the probability distribution, what is the expected number of days per week the captain can leave port?A) 3.7
  B) 4.5
  C) 2.8
  D) 1.7

Q. 5

Frasier and Company manufactures four different products that it ships to customers throughout the United States.
 
  Delivery times are not a driving factor in the decision as to which type of carrier to use (rail, plane, or truck) to deliver the product. However, breakage cost is very expensive, and Frasier would like to select a mode of delivery that reduces the amount of product breakage. To help it reach a decision, the managers have decided to examine the dollar amount of breakage incurred by the three alternative modes of transportation under consideration. Because each product's fragility is different, the executives conducting the study wish to control for differences due to type of product. The company randomly assigns each product to each carrier and monitors the dollar breakage that occurs over the course of 100 shipments. The dollar breakage per shipment (to the nearest dollar) is as follows: Rail Plane TruckProduct 1 7,960 8,053 8,818Product 2 8,399 7,764 9,432Product 3 9,429 9,196 9,260Product 4 6,022 5,821 5,676Was Frasier and Company correct in its decision to block for type of product? Conduct the appropriate hypothesis test using a level of significance of 0.01.A) Because F = 32.12 > F=0.01 = 9.78, reject the null hypothesis. Thus, based on these sample data we conclude that blocking is effective.
  B) Because F = 28.14 > F=0.01 = 7.63, reject the null hypothesis. Thus, based on these sample data we conclude that blocking is effective.
  C) Because F = 32.12 > F=0.01 = 9.78, do not reject the null hypothesis. Thus, based on these sample data we conclude that blocking is not effective.
  D) Because F = 28.14 > F=0.01 = 7.63, do not reject the null hypothesis. Thus, based on these sample data we conclude that blocking is not effective.

Q. 6

The random variable x is the number of customers arriving at the service desk of a local car dealership over an interval of 10 minutes. It is known that the average number of arrivals in 10 minutes is 5.3.
 
  The probability that there are less than 3 arrivals in any 10 minutes is:A) .0659
  B) .0948
  C) .1016
  D) .1239