Some data on the ages (in years) of the consumers of the four cereals appear below. The dataset is stored in the EViews workfile age.wfi. Coco Pops Fibre Plus Nutrigrain ni = 63 n3 = 40 n4 = 111 33 27 25 Special K n2 = 81 26 31 25 39 39 33 39 40 42 (a) Using EViews, construct histograms of the ages of the consumers for each brand of cereal. From the constructed histograms, report the sample means and the standard deviations for each brand of cereal. 3 (b) Assuming that the unknown population variances are equal and the data are normally distributed, can you conclude at the 5% significance level that age of the consumers varies among the four cereals? Your answers must be calculated manually using the sample statistics provided in part (a). 20 Series: COCO_POPS Sample 1 111 Observations 63 16 12 Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis 31.30159 31.00000 55.00000 25.00000 5.323820 1.482986 7.348321 8 4 Jarque-Bera Probability 72.72533 0.000000 0 25 30 35 40 45 50 55 9 8 Series: FIBRE_PLUS Sample 1 111 Observations 40 7 6 5 4 Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis 37.37500 37.50000 48.00000 25.00000 5.582424 0.002029 2.532856 3 2 1 Jarque-Bera Probability 0.363733 0.833713 0 25.0 27.5 30.0 32.5 35.0 37.5 40.0 42.5 45.0 47.5 50.0 20 Series: NUTRIGRAIN Sample 1 111 Observations 111 16 12 Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis 39.92793 40.00000 68.00000 25.00000 8.487115 0.251514 2.872114 8 4 Jarque-Bera Probability 1.245939 0.536349 0 25 30 35 40 45 50 55 60 65 70 12 Series: SPECIAL_K Sample 1 111 Observations 81 10 8 6 Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis 34.41975 35.00000 45.00000 25.00000 4.816285 0.030529 2.606374 4 2 Jarque-Bera Probability 0.535510 0.765095 0 26 28 30 32 34 36 38 40 42 44 46 Some data on the ages (in years) of the consumers of the four cereals appear below. The dataset is stored in the EViews workfile age.wfi. Coco Pops Fibre Plus Nutrigrain ni = 63 n3 = 40 n4 = 111 33 27 25 Special K n2 = 81 26 31 25 39 39 33 39 40 42 (a) Using EViews, construct histograms of the ages of the consumers for each brand of cereal. From the constructed histograms, report the sample means and the standard deviations for each brand of cereal. 3 (b) Assuming that the unknown population variances are equal and the data are normally distributed, can you conclude at the 5% significance level that age of the consumers varies among the four cereals? Your answers must be calculated manually using the sample statistics provided in part (a). 20 Series: COCO_POPS Sample 1 111 Observations 63 16 12 Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis 31.30159 31.00000 55.00000 25.00000 5.323820 1.482986 7.348321 8 4 Jarque-Bera Probability 72.72533 0.000000 0 25 30 35 40 45 50 55 9 8 Series: FIBRE_PLUS Sample 1 111 Observations 40 7 6 5 4 Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis 37.37500 37.50000 48.00000 25.00000 5.582424 0.002029 2.532856 3 2 1 Jarque-Bera Probability 0.363733 0.833713 0 25.0 27.5 30.0 32.5 35.0 37.5 40.0 42.5 45.0 47.5 50.0 20 Series: NUTRIGRAIN Sample 1 111 Observations 111 16 12 Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis 39.92793 40.00000 68.00000 25.00000 8.487115 0.251514 2.872114 8 4 Jarque-Bera Probability 1.245939 0.536349 0 25 30 35 40 45 50 55 60 65 70 12 Series: SPECIAL_K Sample 1 111 Observations 81 10 8 6 Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis 34.41975 35.00000 45.00000 25.00000 4.816285 0.030529 2.606374 4 2 Jarque-Bera Probability 0.535510 0.765095 0 26 28 30 32 34 36 38 40 42 44 46