Reference no: EM132725569

Write analysis of the each question and the choice of hypothesis with justifications for each of the question (where needed).

Question 1.
Muscat College arranged a general entry test for the candidates who want to enroll in postgraduate program. Twenty Students with different backgrounds participated in the test and scored as below.

Obtain the five number summary and construct a box and whisker plot of the obtained marks. Also check for the presence of outliers and draw stem and leaf plot.

Question 2.

(a) Write short note on the use/importance of Regression Analysis with at least one example. (Minimum 150 words)

(b) When do we use hypothesis testing? Explain with real life examples. (Minimum 150 words)

Question 3.
Over a 4-year period the health and diets of 605 heart attack survivors were monitored to determine the effect of a Mediterranean diet on their health post heart-attack. The results were recorded as either the patient died, suffered a non-fatal serious illness or remained healthy throughout the study period and are tabulated below:

By performing an appropriate test, assess formally the assumption that the subject's health post- heart attack is associated with the subject's diet.

Question 4
A sports journalist is interested in whether the average age of professional footballers has changed. In order to try and answer this question he collects information on the ages of footballers playing in the English football leagues in 1960 and 1998. He selects a random sample of 17 footballers playing in the First Division in 1960, and a random sample of 17 footballers playing in the Premier League in 1998.

First Division, 1960 (x)
24 31 25 24 29 27 23 23 30 24 25 25 21 30 29 28 24

Premier League, 1998 (y)
21 24 18 23 29 21 24 19 23 26 23 27 34 25 19 24 26

Summary Statistics
∑ x_i = 442 , ∑ y_i = 406
∑ x_i² = 11634, ∑ y_i² = 9946

Carry out a formal test of the equality of the population variances. State clearly your conclusion.

Question 5.

A random sample of 24 ten year old children was randomly divided into four groups in order to study pattern recognition skills. Each child is given a pattern recognition test with 10 patterns to identify. Children in Group 1 were given praise for each correct answer and no comment on wrong answers; Group 2 were given criticism for each wrong answer and no comment for correct answers; Group 3 were given no praise or criticism but the observer expressed interest in what the child was doing; and children in Group 4 were left on their own to complete the test. The number of correct answers given by each child ( y_ij ; i = 1, ... 4 ; j = 1,...6) are presented below.

∑ ∑ y_ij = 139

∑ ∑ y_ij² = 915

Compare the mean of the correct answers of the four groups and state your conclusion clearly

Question 6.

As part of a study of legibility and visibility of road signs the roads authority wanted to examine the relationship between driver's age and sign legibility distance in order that road safety could be improved for older drivers. Sign legibility is the maximum distance at which the subject could read the road sign. The following are the data for a random sample of 12 drivers between the ages of 17 years and 80 years.

∑ y_i = 4935, ∑ x_i = 588

∑ y_i² = 2102425, ∑ x_i² = 34406

∑ x_iy_i = 225105

Use the Minitab output (Figures 1 and 2 and Table 1) on the next two pages, where appropriate, to answer the questions below

(a) Calculate the correlation coefficient between age and sign legibility distance. Give full details of how you could use the Minitab output to check your answer.

(b) Using the Minitab output, carry out an appropriate test to investigate whether there is a linear relationship. Give full details of the hypothesis test and calculate a 95% confidence interval that could also be used to test the hypothesis.

(c) Discuss how good the model is in relation to your answers in (a), (b) and the Minitab output.

Table 1.

Regression Analysis

The regression equation is y=558-2.99x

S=47.9493,    R-Sq=68.5%,    R-Sq (adj)=65.3%