Question

Question 1

In each of the following situations, identify the population and the sample

(i).There are 50 books in statistics in our library which contains a collection of 5,000 books.

(ii).About 20% of the stones heaped on the building site are round in shape.

(iii).The dream that there will be more female than male politicians in Ghana will never be realized

(iv) About 10% of pregnant mothers reporting to hospitals are infected with HIV virus.

(v) Since the last major earthquake in 1939, there have been 60 earth tremors in Ghana, with 20 these occurring over the past 5 years.

Question 2

In each of the following situations, identify the scale(s) of measurement that is appropriate for each situation.

(i) A visiting school inspector asked a class teacher to rank the thirty students in her class on “level of discipline”, with 1 standing for the least disciplined student and 30 standing for the most disciplined student.

(ii)   Identical twins living in different environments are being compared to find out the influence of the environment on their academic performance. A standard test on academic performance is giving to fifty (50) sets of identical twins and their performance graded over 100.

(iii) “Regular” students and students admitted under the distance learning programme into Accra Institute of Technology are administrated a questionnaire measuring “level of maturity” of the students, with scores on “level of maturity” ranging from 0 to 1

(iv) One thousand students in a statistics class are asked to rate their lecturer on teaching effectiveness at the end of the semester, where rating scores on teaching effectiveness can possibly range between 10 and 50.

(v) A relationship is to be established between “Campus of Study” and “Academic Performance” among Accra Institute of Technology students at KCC campus and Seaview campus based on their final grade point average (FGPA), classified as “Good” (FGPA of 3.2 or better), “Average” (FGPA of 2.5 to 3.19) or “Poor” (FGPA below 2.5). Five hundred (500) and 100 students are sampled from KCC campus and Seaview campus respectively. Out of the 500 students sampled from KCC campus, 200 were classified as “Good” as “Average” and the rest as “Poor”. Out of the 100 students sampled from Seaview campus, 30 were classified as “Good”, 40 as “Average”, and the rest as “Poor”.

Question 3

There are three insurance companies in the Business District in Accra. It is known from previous records   that each year, 2 percent, 5 percent and 3 percent of those insured by Vanguard Insurance, Enterprise Insurance and Star insurance respectively submit claims. 20 percent of the people in the community have an insurance policy with Vanguard Insurance Company, 30 percent with Enterprise Insurance Company and 50 percent with Star Insurance Company.   

(i) What is the probability that a randomly selected insurance policyholder in the community did a claim in a certain year?    

(ii) If a randomly selected policy holder in the community is found to have made a claim in a certain year, what is the probability that, that person is insured with Vanguard Insurance?

(iii) If a randomly selected policy holder in the community is found to have made a claim in a certain year, what is the probability that, that person is insured with Enterprise Insurance?           

Question 4

Using practical examples from the field of statistics, determine the following variables you expect to have a normal or nearly normal distribution. Illustrate by discussing and explaining possible reasons for your answer.

a. Scores on a very easy test

b. Shoe sizes of a random sample of adult women

c. The number of apples in each of 100 full bushel baskets

Answer 1

Question 1). Population contain the whole elements, categories and value of the data set whereas sample are the some derived part of population.. Now,

(i) Here our population is total number of books in the library that is 5000 whereas our sample is number of books of statistics in library that is 50.

(ii) Here our population if types of stones at building site whereas our sample is round shaped stones at building site which is 20%.

(iii). Here our population is total number of politicians in Ghana (both male and female) whereas our sample is number of female politicians in Ghana.

(iv). Here our population is total number of people affected with HIV whereas our sample is pregnant number of women's which are affected with HIV which is 10%.

(v). Here our population is total number of earthquake occured in Ghana till now which is 60, whereas our sample is number of earthquake occurred in Ghana in past 5 years which is 20.