# Statistical Inference and Standard Deviation Essay

Question 1. (Descriptive Statistics) Investment Returns:These data are the annual returns on shareholders’ funds of 97 of Australian’s top 100 companies for the years 1990 and 1998. (i)Produce a histogram of the 1990 returns. (ii)Produce a histogram of the 1998 returns. (iii)Find the mean, median, range and standard deviation for the 1990 returns. Annual Returns % (1990) Mean12. 91865979 Median11. 38 Standard Deviation9. 297513067 Range75. 01 (iv)Repeat part (iii) for the 1998 returns. Annual Returns % (1998) Mean6. 355463918 Median5. 4 Standard Deviation5. 170830853 Range42. 76 (v)Which was the better year for investors? 1990 was the better year for investors in regards to annual returns being consistent with the mean of 12. 9% compare to 6. 4% for 1998. •The measure of variability was high in 1990 with the range of 75. 01 compare to 42. 76 for 1998. Another high variability for 1990 was the standard deviation of 9. 30 compare to 5. 17 for 1998. (For Excel instructions see pages 28 and 61 of the textbook. ) Question 2. (Statistical Inferences: Single Population) Feasibility Study: Companies that sell groceries over the Internet are called e-grocers. Customers enter their orders, pay by credit card and receive delivery by truck.

To determine whether an e-grocery would be profitable in one large city, a potential e-grocer offered the service and recorded the size of the order for a random sample of customers. The data are stored in the data file. (i)Estimate with 95% confidence the average order in the city. Orders (\$) Mean89. 16511905 Confidence Level (95. 0%)3. 770623926 (ii)Financial analysis indicates that to be profitable the average order would have to exceed \$85. Can we infer from the data that an e-grocery will be profitable in the city? Test using ? = 0. 01. Step 1: Hypothesis is that to be profitable the average order has to exceed \$85.

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Since it’s unproven, it is the alternative hypothesis. The null hypothesis is still \$85. H0: µ = 85 Ha: µ > 85 Step 2: Statistical test to be used is data analysis of one-sample t test for means with unequal variances. Step 3: The value of alpha is 0. 01. Step 4: t Critical one tail = 2. 351, the decision rule is to reject the null hypothesis if the observed test statistic is greater than 2. 351. Step 5: The gathered data are shown t-Test: One-Sample Assuming Unequal Variances Orders (\$) Mean89. 16511905 Variance301. 8934831 Observations84 Hypothesized Mean Difference0 df150 t Stat14. 28109759 P(T

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