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BCO127 Applied Management Statistics

Task

The task is an individual task.

You must answer all questions.

Once you have answered the questions, upload your answers to Moodle.

YOU MUST SHOW ALL YOUR CALCULATIONS

Answer to 2 decimal places

Formalities:

• Wordcount: N/A
• Font: Arial 12,5 pts.
• Text alignment: Justified.

Weight: This task is a 40% of your total grade for this subject.

It assesses the following learning outcomes:

• Outcome 1: understand concepts, formulas and techniques of statistics through exercises and applied examples;
• Outcome 2: design statistical models, perform analysis, and solve real-world problems;
• Outcome 3: interpret results of statistical analysis.

Task

Resolve the following problems, show all calculations.

1. A snack company sells mixed nuts. It claims peanuts make up 13% of the content by weight. A manager wishes to find out if the actual content of peanuts in the packet is what it states on the packet. State the null and alternative hypotheses to check if the packets actually contain 13% peanuts. (10%)
2. A company undertakes regression analysis to determine if there is correlation between number of customers in catchment area (measured in millions) and annual sales (measured in millions of dollars). After charting the data, excel returns a correlation equation of:

y = -1.20 +2.05x

If the number of customers in a catchment area is 3.7 million, what is the predicted level of sales? (10%)

3. The mean production rate for a factory is known to be 31 units per hour, with a standard deviation of 5.5 units. A modification is made to the production line. After the modification the production rate is seen to rise to 33.8 units per hour, based on a sample of 35 tests. Is there any evidence at the 95% level of significance that productivity has improved? (20%)
4. Your company packs coffee into 10 kg packs. From a sample of 6 packs, you obtain a mean weight of 9.51 kg. What is the 95% confidence interval if is known that the weight of coffee packs is normally distributed and the standard deviation is 0.55 kg? (20%)
5. A manufacturer of miniature servo-actuators for models claims their motors last for 7500 hours. It is known that the standard deviation is 1000 hours, and that the distribution is normal. If a random sample of 64 motors is taken, with a mean of 7250 hours, is their evidence that the mean is no longer 7500 hours? (20%)
6. You believe that spending on clothes amounts to at least 500 euros per year. You know that clothes spending follows a normal distribution, with a standard deviation of 60. You undertake a random sample of 49 students, and they report spending 480 euros. You wish to test your hypothesis at α=0.05. From your research, is spending on clothes at least 500 euros? (20%)