BBM203 Business Statistics Assignment 1 Instructions Assignment 1 covers the topics in Probability and Hypothesis Testing

BBM203 Business Statistics Assignment 1

Instructions

1. Assignment 1 covers the topics in Probability and Hypothesis Testing.

2. Assignment 1 contains:

FIVE questions

Answer all questions.

3. The total marks for Assignment 1 is 100 which is equivalent to 50% of your final total marks.

4. All students must submit the T-DF Assignment Declaration Form as the front cover when you submit your assignment.                         

5. The deadline for the submission of Assignment 1 is on 6 March 2021 before 12.00 midnight. 

1. Time spent serving a customer at a cafe is normally distributed, with

   

    = 7 minutes and ? = 8 minutes. 
   1. If you select a random sample of duration serving twenty five (25) customers, determine the probability that the sample mean is between 6.8 and 7.2 minutes.    

[9 marks]

1. 2. If you select a random sample of 144 customers, determine the probability that the sample mean is between 6.8 and 7.2 minutes.

[6 marks]

1. 3. Explain the difference in the results of (i) and (ii).                              

[6 marks]

2. A factory manager collected a sample of ten (10) packets of 3-in-1 coffee and             the weights (in grams) of each packet are recorded as follow:

                               25    23    26    28    24    

                               21    26    24    25    27

Calculate

[6 marks]

(c) find a 90% confidence interval for the weights of the 3-in-1 coffee.   

[6 marks]

3. A service counter manager wishes to ensure that an average of 16 seconds to serve a customer. In order to analyse the efficiency of the service process, he takes a random sample of 56 customers. The mean service time of the sample is 15.8 seconds. Assume that the population standard deviation is 0.8 seconds.

1. 1. State the null and the alternative hypotheses for the test.                  

[4 marks]

1. 2. Use the p-value approach to test the manager's concern at ? = 0.05. 

                                                                                                               [8 marks]

1. 3. Confirm your result in (ii) by using the critical value approach.          

[6 marks]

1. 4. State the recommendation that the manager can present to the company.   

[3 marks]

4. A survey carried out by John claims that the average cost of living for households in City 1 is more than that in City 2:

1. 1. Specify the competing hypotheses to test John's claim.

                                                                             [4 marks]

1. 2. Calculate the value of the test statistic.                                             

 [5 marks]

1. 3. At the 5% significance level, is John's claim supported by the data? Explain

                          [9 marks]

5. The market shares in 2012 of four (4) television companies, A, B, C and D are listed  below. A survey was carried out in 2017 on 200 television buyers and the distribution of buyers to A, B, C and D are also listed in the last column.

1. 1. Specify the competing hypotheses to test whether the market shares have    changed since 2012.

[6 marks]

1. 2. Calculate the value of the test statistics.

[10 marks]

1. 3. Use ? = 0.05 to determine if the market shares have changed since 2012.

[9 marks]