2. A maker of small appliances recently sampled 200 independent retailers across Canada, recording the retail cost of a popular blender. Also recorded was whether the store also sold groceries (1-yes and 2-no). Use the #2 Data Set. (10 marks) a) Find the 95% confidence interval for the mean cost of the blender. b) Test whether the mean price of the blender is significantly lower than last year's mean of $71.35. c) Test whether the variance of the sample is significantly different than the previously assumed variance of 77.3. 2 d) Find the 90% confidence interval for the proportion of stores which sell groceries. e) Is there significant evidence that more than 45% (the previously assumed proportion) of stores sell groceries? f) Have the required conditions been met for parts a through e? Show your work.

The Data set is as follows:

Blender Price 83.51 80.97 81.16 84.4 72.16 81.22 74.64 81.72 83.99 81.01 69.19 66.92 70.55 69.32 76.84 71.72 84.32 82.77 79.13 76.28 74.17 75.99 73.26 75.2 72.47 66.59 94.03 76.39 70.15 75.41 82.1 72.45 72.5 68.5 75.36 72.48 71.77 70.3 68.25 70.03 70.83 82.37 81.22 63.18 74.72 76.59 80.62 63.23 59.93 77.73 85.99 64.71 78.99 82.42 74.53 66.87 73.98 76.01 68.14 81.73 69.38 74.13 76.09 86.66 78.9 74.35 74.64 67.03 62.92 73.27 80.17 83.09 70.21 84.32 76.25 71.63 56.27 79.37 87.03 83.71 76.35 83.36 81.66 90.64 73.02 97.74 80.74 75.56 78.67 59.62 83.04 77.55 89.08 73.75 77.43 73.96 73.88 79.34 75.96 79.82 53.87 85.1 72 74.62 85.14 68.23 62.24 65.54 81.84 75.99 73.03 85.5 73.97 65.56 75.99 87.98 75.71 74.24 59.85 78.88 86.07 81.48 61.81 84.33 70.82 80.84 72.28 88.3 78.6 67.45 66.91 65.22 73.1 98.79 71.5 68.46 62.32 69.83 64.17 81.16 84.58 80.69 78.99 68.14 81.24 70.61 86.17 68.42 81.77 75.54 57.76 74.46 74.37 73.96 73.98 77.42 67.36 71.73 69.15 69.74 77.43 70.35 68.64 77.71 74.89 77.75 56.87 74.2 54.34 78.05 67.16 68.85 83.13 76.25 83.45 79.8 90.96 73.3 87.99 72.58 77.49 51.33 75.21 79.78 83.39 79 72.41 74.89 62.94 82.46 77.85 72.43 84.37 78.06 69.32 67.23 65.28 76.52 76.51 75.71

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