Question

Problem Kabul: According to data released by World Bank, the mean PM10 (particulate matter) for the city of Kabul Afghanistan in 2012 was 46. Suppose that because of efforts to improve air quality in Kabul, increases in modernization and efforts to establish environmentally friendly businesses, city leaders believe PM rates have decreased. To test this notion, city leaders randomly sample 25 readings over a one-year period. The readings are shown below. Set alpha to .10 Kabul PM Data (enter into Minitab column) 36 54 55 53 57 47 42 40 45 38 53 45 47 22 25 46 34 62 54 55 44 34 51 54 27 Instructions to get you started: Enter data from problem into a Minitab worksheet to create a dataset for the Kabul PM data. Use Minitab to test the hypothesis you formulate for the Kabul study. Present your work in report format using the six-step process demonstrated in class and which is shown on the final page of this handout For your report (prepared in Word) you will need a Problem Definition, a Hypothesis (use correct symbols in Word see INSERT>Symbols for the correct symbols to use in the hypothesis) a Decision Rule (use tables to determine the correct critical value, for the Conclusion section include the critical value/critical ratio technique, the confidence interval technique the p-value technique to test the null hypothesis State the type of error you may have made. For the Interpretation section state whether the air quality has improved or has stayed the same. For you Assumption section; address the assumption of normality by referencing the boxplot of the data. Be sure to cut and paste the graph form Minitab to your report. Resize the graph to fit neatly within your report in the section you label Assumptions. Include a brief discussion of how normality is or is not satisfied according to what you see in the graph. At minimum, be sure to reference the median and mean and central tendency or your discussion of the graph. Be sure to discuss direction of skew

Answer 1

From Given data,

Mean (xbar) = 44.8

Std Dev (s) = 10.62

n = 25

Standard Error(SE) = s/n^1/2 = 2.12

Alpha = 0.1

Null and Alternate Hypothesis

H₀: µ = 46

H_a: µ < 46

Decision Rule

If the p-value < alpha, reject the null hypothesis

Test Statistic

t = (xbar - µ₀) / SE = (44.8-46)/2.12 = -0.56

p-value = TDIST(0.56,24,1) = 0.289

Since the p-value is greater than 0.1, we fail to reject the null hypothesis ie mean PM10 is 46.

We might have made a Type II Error as a type II error is the failure to reject a false null hypothesis.

Since the mean and median are almost in the centre, this validates the assumption that the sample comes from a normal distribution.

The value for skewness is -0.61 which represents moderately skewness.