Question

The world is currently being adversely affected by the COFLU-20 pandemic. Persons are required to take certain measures to prevent the spread of this virus; however, persons’ knowledge, attitudes and practices towards COFLU-20 may influence their adherence to these measures.

A researcher decided to evaluate the knowledge, attitudes and practices towards COFLU-20 of adults living in the English-speaking Caribbean. To gather the data, the researcher developed an online survey consisting of four (4) sections. Section A gathered demographic data on the respondents including their gender, marital status, highest level of education attained, occupation and country of residence. Section B consisted of 15 questions that gathered data on the respondents’ knowledge of COFLU-20. Section C consisted of 10 questions that gathered data on the respondents’ attitudes towards COFLU-20. The final section, Section D, consisted of 5 questions that gathered information on the respondents’ practices against COFLU-20.

In order to recruit respondents for this survey, the researcher sent a link to the online survey to persons in his network via email and social media. After receiving 300 responses, the researcher closed down the online survey and deactivated the link to the survey.

You are a student pursuing an introductory Statistics course. The researcher has asked that you assist him in summarizing, analyzing and interpreting the information gathered, by answering the questions below.

QUESTION 1

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(a) (i)   Identify the population of interest for this scenario.                                        [1 mark]

(ii) Identify the sampling technique used by the researcher.                                   [1 mark]

(iii) State one advantage and one disadvantage of the sampling technique described in the given scenario.                                                                                                          [2 marks]

Table below summaries the age group of the 300 respondents.

Table 1

Age Group	Number of Respondents
18-25	62
26-34	60
35-44	55
45-54	70
55 - 75	53

(b) Use the data given in Table 1 to:

continue overleaf…/

(i) calculate the mean age of the respondents                                                   [3 marks]

(ii) identify the modal interval and interpret your answer                                [2 marks]

(iii) identify the median interval                                                                      [1 mark]

Each respondent was given a score, from 1 to 15, on his or her knowledge of the COFLU-20. A score from 1 to 7 was considered to indicate ‘poor’ knowledge, 8 to 11 indicated ‘satisfactory’ knowledge and 12 to 15 indicated good knowledge. Table 2 below shows the knowledge level of respondents, by age group.

Table 2

Age Group		Knowledge Level			Total
		Poor	Satisfactory	Good
	18 - 25	33	16	13	62
	26 - 34	30	18	12	60
	35 - 44	29	14	12	55
	45 - 54	36	16	18	70
	55 - 75	17	14	22	53
Total		145	78	77	300

(c) Using Table 2, assist the researcher to calculate the probability that a randomly selected respondent:

(i) is below 35 years of age and has good knowledge of the COFLU-20          [2 marks]

(ii) is below 35 years of age or has good knowledge of the COFLU-20            [3 marks]

Total 15 marks

QUESTION 2

To examine practices towards COFLU-20, the researcher examined the relevant responses from the survey and assigned scores of 1 (below required standard), 2 (poor standards), 3 (satisfactory standards), 4 (meets required standards) and 5 (exceeds required standard) to each respondent. Using X to represent the score for practices against COFLU-20, the probability distribution of X is shown in Table 3 below.

Table 3

x	1	2	3	4	5
P(X =x)	0.21	0.197	0.2	0.173	0.22

continue overleaf…/

The researcher is interested in using the information in Table 3 to determine the probability that, from a sample of 10 randomly selected adults, exactly 3 of them exceeds the required standard for practices towards COFLU-20.

(a) Assist the researcher by:

(i) carefully defining the random variable of interest                                          [1 mark]

                       

(ii) identifying a suitable probability distribution to be used to find the probability that exactly three (3) adults, out of 10, exceeds the required standard for practices towards COFLU-20. State the value(s) of the parameter(s) for this distribution.                                     [3 marks]

(iii) justifying the suitability of the probability distribution identified in part (ii)                                                                                                                                               [4 marks]

(iv) calculating the probability that exactly 3 adults, out of 10, exceeds the required standard for practices against COFLU-20                                                                                   [2 marks]

(b) Individual scores for practices towards COFLU-20 are found to be normally distributed with a mean of 3 and a standard deviation of 1.5 over the entire population. The Ministry of Health wishes to use this information to identify individuals whose score on practices towards COFLU-20 is in the lower 75%, in order to give them relevant information on the best practices towards COFLU-20. You are asked to assist in calculating the score that the Ministry of Health should use to decide whether an individual should be given the relevant information?       [5 marks]

Total 15 marks

Answer 1

Question 1:
(a) (i) The population here is the adults living in the English-speaking Caribbean.
(ii) The sampling method used here is convenience sampling.
(iii) The one advantage of this sampling method is that it takes a short duration of time to gather data and information. The one disadvantage is that it is highly vulnerable to selection bias and influences beyond the control of the experimenter.
(b) (i) We calculate the midpoint of the age groups, which are called class marks (m) of class intervals. These class mark values are = (21.5, 30, 39.5, 49.5, 65). The corresponding frequencies (f) are = (62, 60, 55, 70, 53). The mean age of respondents = sum(m * f)/sum(f) = 40.72.
(ii) The modal interval is 45-54 because it has the highest frequency (number of respondents).
(iii) The total number of respondents is 300. The corresponding cumulative frequency of less than type for the different age groups is = (62, 122, 177, 247, 300). Now, the mid-value of the total no. of respondents is 150 which is less than the cumulative frequency of 177 and it is corresponding to the 35-44 age group. Hence, 35-44 is the median interval.
(c) (i) No. of respondents who are below 35 years of age and has good knowledge of the COFLU-20 = 13+12 = 25. Hence, required probability = 25/300 = 0.0833.
(ii) No. of respondents who are below 35 years of age = 62+60 = 122.
No. of respondents who have good knowledge of the COFLU-20 = 77.
Hence, required probability = (122+77-25)/300 = 0.5800.

Question 2: