Question 1

a) Apply the necessary transformation in PSPP/SPSS using the relevant variables from the data file to create two new variables, 1) Number of Days in the Month and 2) Decade. Identify the appropriate scale of measurement for both variables, and generate the frequency distribution tables for both variables. Cut and paste the PSPP/SPSS outputs into your answer.

Note: For the Number of Days in the Month, please remember to take into account leap years.

Note: For Decade, please use the 0-to-9 decade denomination to group the years.

b) Apply PSPP/SPSS to examine the appropriate descriptive statistics and graph(s) for Total Rainfall separately by Months of a Year, Yearly, and Decade. Interpret the results in terms of the appropriate descriptive statistics and identify the Month(s), Year(s) and Decade(s) with the highest and lowest Total Rainfall.

Note: Please cut and paste your PSPP/SPSS output into your answer to demonstrate that you have used PSPP/SPSS.

Note: The appropriate descriptive statistics might differ for Months of the Year, Yearly or Decade.

Question 2

a) Apply PSPP/SPSS on the Total Rainfall to calculate the z-scores of each data point (a case) based on i) sample mean and standard deviation and ii) respective monthly means and standard deviations. Generate the frequency distribution tables for both z-scores and paste the first 10 entries and last 10 entries of the frequency distribution table from your PSPP/SPSS output into your answer.

Note: Please cut and paste your PSPP/SPSS output into your answer to demonstrate that you have used PSPP/SPSS.

Note: If you are unable to calculate the z-scores using PSPP/SPSS but are able to calculate with other means, please provide your answers as well as a short description of how you do the calculations.

b) Using your understanding of z-scores, examine the differences in the interpretation of the two types of z-scores calculated in Q2a.

c) The market researcher is interested to predict what the Total Rainfall would be like for January 2020. Apply the necessary formulas to calculate the i) probability that the Total Rainfall for January 2020 is 280mm or higher, and ii) range for Total Rainfall for the middle 80% of all possible values.

Note: Please show the necessary calculations in your answers. You may want to use the concepts of standard error, critical value and proportions in body and tail of distribution to help you answer this question. Round off your final answers to the nearest whole number.

Note: The sample means and standard deviations may be used in lieu of population means and standard deviations.

Question 3

A colleague of the market researcher argued that the Number of Days that Rained is a better indicator of wetness and dryness of a month.

a) Apply PSPP/SPSS to examine the appropriate descriptive statistics for Number of Days that Rained separately by Months of a Year and determine if the wettest and driest months defined by Number of Days that Rained are the same or different as the wettest and driest months defined by Total Rainfall as examined in Q1b.

Note: Please cut and paste your PSPP/SPSS output into your answer to demonstrate that you have used PSPP/SPSS.

b) Examine the appropriateness of either Total Rainfall or Number of Days that Rained as a measure of wetness/dryness.

c) Identify one issue with using either Total Rainfall or Number of Days that Rained to indicate wetness/dryness in a month and recommend how this issue can be resolved. Analyze the data with your solution and determine if the wettest and driest Months are the same or different as Q1b and Q3a.

Note: Please cut and paste your PSPP/SPSS output into your answer to demonstrate that you have used PSPP/SPSS.