Question 1

A physiotherapist in a private hospital located in Selangor would like to do a study on patients diagnosed of having Scoliosis problems. Their heights (in cm) were recorded and are approximately normally distributed. The recorded data is shown in the following table.

• Use any statistical software to generate the descriptive statistics for the above data. The statistics generated should include the values of the sample mean, sample standard deviation, and sample size.
• From the output generated in (a), state the mean and interpret its value in terms of the case study.
• Use 𝑝-value to test whether the population means the height of patients diagnosed having Scoliosis problems is different from 170cm at α = 0.05. You should include a statistical output in your answer.
• If a private hospital located in Perak has historical data of Scoliosis patients having a mean of 175.56 cm and a standard deviation of 1.5 cm, data of which hospital is more consistent? Justify your answer.

• Question 2

  A study was conducted to determine if there is a significant difference in the density of organisms at two different stations. The following data give the density measurements, in the number of organisms per square meter, at the two collecting stations.

  

  Assume that the distributions for both populations are normally distributed and 𝛼=0.05. Answer the following questions using the data given in the above table. You may use any statistical output from any software to help you solve the following problems.

  • Generate the statistical output(s) to test if there is a difference in the mean number of organisms per square meter between the two stations. Your output(s) should include Levine’s Test for Equality of Variances, values of the confidence interval, test statistic, and p-value. Answer the following questions based on your generated output(s).
  • Use the output(s) in (a), and answer the following questions:

  (i) Based on Levine’s Test for Equality of Variances statistics, test on the assumption of variances that are required to test the difference in the mean number of organisms per square meter between the two stations. Show your work, justification, and conclusion clearly.
  (ii) Verify the values of the confidence interval for the difference in two populations in your output by calculation.
  (iii) Conduct a hypothesis test to see if there is a difference in the mean number of organisms per square meter between the two stations. Conclude your test clearly in the context of the problem.

  Question 3

  Ten pilots were tested in a flight simulator before and after completing the hours of fly, and the time for each to complete a certain corrective action was measured in seconds, with the following result;

  

  (a) Presentasuitable statistical output to perform a one-tailed Paired T-Test for the above data.
  (b) Use the output to test if the pilot has improved after completing the hours of flight at α = 0.05.