Quiz 2: A Review of Basic Statistical Concepts

Business

a. Obtain the mean and standard deviation using MINITAB procedure. MINITAB procedure: Step 1: Choose Stat Basic Statistics Display Descriptive Statistics. Step 2: In Variables enter the column of Prices. Step 3: In Statistics , select Mean , StDev and N Number. Step 4: Click OK. MINITAB output: img From the MINITAB output, the mean price img is img and the standard deviation img of the prices is img .

a. Obtain the mean percent earnings for the population of jobs by using MINITAB. MINITAB procedure: Step 1: Choose Stat Basic Statistics Display Descriptive Statistics. Step 2: In Variables , enter Earnings. Step 3: In Statistics , select Mean and StDev. Step 4: Click OK. MINITAB output: img From the above MINITAB output, the point estimate mean percent earning img for the population of jobs is img . b. Obtain a 95% confidence interval for the mean percent earnings for the population of jobs using a large-sample argument. The level of significance is 0.95. img From the table B-2, the table value of img is given below: img The general formula for the confidence interval estimate for population mean using large- sample argument is img Obtain standard deviation by using MINITAB. From the above MINITAB output in part (a), the standard deviation img is img . The 95% confidence interval is obtained below: Substitute, img , img , img and img . img Therefore, the 95% confidence interval for mean percent earning for population of jobs lies between img . c. Obtain a 95% confidence interval for the mean percent earnings for the population of jobs using a small-sample argument. From the table B-3, the table value of img with img degrees of freedom is given below: img Thus, the value of img is img . The 95% confidence interval is obtained below: img Thus, the 95% confidence interval for the mean percent earning for the population of jobs is img . The additional assumption that is made in this case is that the mean percent earnings are approximately normally distributed. d. Explanation: From part (b) and (c), it is clear that the confidence intervals are approximately same. This is because the multipliers 1.96 and 2.045 are almost has the same magnitude.

a. Obtain the point estimate of the mean img . The sample mean img is the point estimate of the mean img . img Therefore, the point estimate of the mean img is img . Obtain the 95% error margin. It is given that 95% confidence interval for the mean profit per transaction is img img Therefore, the 95% error margin is img . b. Obtain the 90% confidence interval for the mean img . For, the two-tailed test, img From Table B-2, the required img value for 90% confidence level is, img Thus, the 90% confidence interval is obtained below: img Therefore, the 90% confidence interval for the mean profit per transaction is img .