Question

1. A video game company is interested in knowing the population mean number of hours spent playing a new game from start to finish. If the game takes longer than 50 hours to play, on average, then it will need to be re-worked. The company collects a sample of 49 video game players with various levels of expertise, and finds that it takes them 48 hours, on average, to complete the game, with a standard deviation of 1.5 hours.
   
   1. Conduct an appropriate hypothesis test using the critical value method. [7 marks]
      
   2. Explain what a Type II Error means in this context. [1 mark]
      
2. A major furniture company has a line of couches designed for apartment dwellers. These couches need to be light enough to be carried up flights of stairs. The lead engineer wants to use a new type of material. The engineer claims that the new couches will be lighter than the old couches.

They take a sample of 10 couches manufactured using the old material and compute an average weight of 350 lbs with a standard deviation of 20 lbs.

They take a sample of 10 couches manufactured using the new material and compute an average weight of 340 lbs with a standard deviation of 15 lbs.

2. 1. Conduct an appropriate hypothesis test using the p-value method. Use the old material as population 1. [8 marks]
      
   2. How much evidence is there against the null hypothesis in part (a)? [1 mark]
      
   3. Explain what a Type I Error means in this context. [1 mark]
      
3. A chocolate company markets a 500g box of chocolates to large retail stores for Valentine’s Day. This year, they project the mean order quantity will be greater than last year. Last year, the mean order quantity was 500 boxes per large retail store. This year, a random sample of 4 large retail stores gave a sample mean order quantity of 490 boxes. Assume a population standard deviation of 50 boxes, and that the mean order quantity follows a Normal distribution.
   
   Conduct a hypothesis test using the critical value method to determine whether this year’s population mean order quantity is more than 10% lower than last year’s. HINT: What is meant by “more than 10% lower”? For example, it might be 10.8885% lower, or 14.68% lower, etc. What does that mean in terms of “number of boxes”? You have to figure that out to answer this question. [7 marks]
   

Answer 1

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