Answer 1
Bias: In research Bias can be defined to select an object or persons over another. The preference for certain objects / persons is higher than other thus trying to change the outcome of a research. The different types of Bias are sampling bias; measurement bias and non-response bias.
An example of selection bias – a researcher wants to the study the birth weight of child born to smoking vs non-smoking mothers. The researcher instead of collecting data from the maternal hospital collects data from other places.
Odds: It is defined as the probability that an outcome of a research may happen or may not happen.
An example -the odds of selecting aces in a pack of card is 1:13.
Favourable Outcome: The outcome which the researcher prefers.
An example of favourable outcome – a player wants to have aces in a selection of cards. If he selects all aces then it is favourable outcome.
Data: The information collected to do any research is data. It may be either numerical or categorical.
Data – the age of the respondents
Answer 2
The sample space is the number of cards
Thus, the number of elements = 52*51 = 2652
Thus, the number of elements without replacement = 2652/2 = 1326.
The elements could be any two cards like 5 and 8
The sample space is any combination of the cards
The number of elements with replacement = 52^3 = 140608
The sample space for the rolling a fair dice is equal to all the outcomes of the dice.
The number of outcomes of a fair dice = 6
The number of outcomes of a coin = 2
Thus, the total number of elements = 6*2 = 12
Answer 4
The probability that Manpreet is in winning team of basketball = 75%
The probability that all friends will play basketball = 40%
Thus, the odds in favour of Manpreet = 40% * 75% = 30%
Answer 5
In a deck there are 52 cards i.e., 4 types with 13 ranks
By pulling out all 9’s and 10’s the number of cards pulled = 2*4 = 8
There are 2 red colours.
By pulling out red aces, the number of cards pulled = 2
Thus, total number of cards in the modified pack = 52 – 8 – 2 = 42
The total number of cards in the deck = 42
The number of hearts = 10
The probability of 3 hearts = 10C3
The number of diamonds = 10
The probability of 2 diamonds = 10C2
The number of spades = 11
The probability of selecting 2 spades = 11C2
The number of club = 11
The probability of selecting 1 club = 11C2
Answer 7
Part a
Number of children
Part b
Height of a person
Part c
Gender
Answer 8
Bias refers to prejudice against any object. In statistics, bias can be introduced in the data collection process. Thus, the population under study is as defined in the research methodology. However, since it is not possible to collect data from the whole population, hence data is collected from a small sample. The sample thus is a representative of the population. If data is collected from certain sections of the population, then the sample is not a true representative of the population. Thus, the outcome of such a study would be biased.
Biased is against the ethics of normal research.
a. Simple random sampling: In this process every individual of the library has affair chance of being selected. Thus, any of the 25 people can be selected at random for the study.
b. Systematic random sampling: The probability sampling method is another form of simple random sampling. Thus, the researcher can arrange the list on the basis of their unique identity and select every 100th person to get 25 people.
c. Stratified random sampling: When the data is collected by segregating into strata then it is stratified random sampling. The 2500 members can be clustered based on the subject of study. Let’s assume that there are 25 clusters. Thus, 1 person is selected at random from each of the clusters
d. Cluster random sampling: The total number of members are clustered into small groups. Each cluster is a representative of the complete population. From any of the clusters 25 people are selected.
e. Multistage random sampling: The total number of members are clustered into small groups. Each cluster is a representative of the complete population. Some of the clusters are selected at random. The process is repeated till we get 25 people.
Answer 10
Sampling bias could be introduced if the data is taken from adults who visit the bakery section.
A survey is conducted in the supermarket. Most of the respondents return the form without answering any questions of providing partial answers.
The survey questions needs to be framed in an unambiguous pattern. On the other hand, if the survey questions are such framed that by the respondents would always answers in yes, then it can be considered as response bias.
In the supermarket if the weights are not calibrated properly then measurement bias would occur. Thus, the purchasers would either get higher amount or would get lower amounts.
Answer 11
The respondent might not be in the age group between 20 – 34 years.
The respondent might not be interested in giving the response.
The three age groups are the strata.
The table
| Age 20-24 | Age 25-29 | Age 30-34 | Total | |
| Yes | 45 | 80 | 5 | 130 |
| No | 25 | 25 | 15 | 65 |
| No response | 25 | 10 | 55 | 90 |
| Total | 95 | 115 | 75 | 285 |
Probability that a person is in the age group of 25-29 = 115/285
Probability that a person gave no response = 90/285
Thus, the probability that a person is in the age group of 25 – 29 or gave no response = 115/285 + 90/285 = 205/285
The probability that a respondent answered the question = (130+65)/285 = 195/285 = 0.68
Thus, the probability that all three respondents answered the questions = 0.68^3 = 0.3144
Hence, the probability that there is one non-response = 1 – 0.3144 = 0.6856
The probability that people need change =130/285 =0.456
Further, the probability of no response = 90/285 = 0.316
Since, in the research a significant portion of the respondents did not provide any response hence clear conclusions cannot be drawn.
90% of those who did not respond do not want change
Thus, 10% of non-response want change.
Hence, the proportion who want change =0.456 + 0.10*0.316 = 0.4876
Thus, the proportion who do not want change = 1 – 0.4876 = 0.5124
Hence, a higher proportion do not want change.
