# Quiz 2: A Review of Basic Statistical Concepts

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: From the MINITAB output, the mean price is and the standard deviation of the prices is .

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: From the above MINITAB output, the point estimate mean percent earning for the population of jobs is . 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. From the table B-2, the table value of is given below: The general formula for the confidence interval estimate for population mean using large- sample argument is Obtain standard deviation by using MINITAB. From the above MINITAB output in part (a), the standard deviation is . The 95% confidence interval is obtained below: Substitute, , , and . Therefore, the 95% confidence interval for mean percent earning for population of jobs lies between . 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 with degrees of freedom is given below: Thus, the value of is . The 95% confidence interval is obtained below: Thus, the 95% confidence interval for the mean percent earning for the population of jobs is . 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 . The sample mean is the point estimate of the mean . Therefore, the point estimate of the mean is . Obtain the 95% error margin. It is given that 95% confidence interval for the mean profit per transaction is Therefore, the 95% error margin is . b. Obtain the 90% confidence interval for the mean . For, the two-tailed test, From Table B-2, the required value for 90% confidence level is, Thus, the 90% confidence interval is obtained below: Therefore, the 90% confidence interval for the mean profit per transaction is .