Business Statistics and Research Methods Questions and Answers

Answer: C

It is the scientific method.

The scientific method is a systematic process of investigation: observing a problem, forming hypotheses, testing them by observation or experiment, evaluating and interpreting the results, and building theory from them. Research in commerce and the social sciences follows the same logic.

A survey and an experiment are particular techniques used within the scientific method, and meta-analysis is a statistical method of combining the results of several studies. None of them is the whole systematic process the question describes.

Answer: C

The probability of drawing a red ball is 0.4.

\[ \begin{aligned} P(\text{red}) &= \frac{\text{red balls}}{\text{total balls}} \\ &= \frac{4}{10} = 0.4 \end{aligned} \]

0.6 would be the probability of a green ball. 0.5 assumes the two colours are equally likely, 0.1 is the chance of one particular ball, and 1.0 would mean drawing red was certain.

Answer: A

It is probability sampling.

In probability (random) sampling every member of the population has a known, calculable and non-zero chance of selection. This allows the sampling error to be estimated and results to be generalised to the population. Simple random, stratified, systematic, cluster and multistage sampling are its forms.

Non-probability sampling, such as quota, convenience and judgement sampling, does not give every member a known chance. Multistage sampling is one design within probability sampling, not the general name the definition describes.

Answer: D

The Mann-Whitney U test is used for testing the equality of two sets of ranking.

It is a non-parametric test for comparing two independent samples. The observations from both samples are ranked together, and the test checks whether the ranks are distributed alike in the two groups, that is, whether the two samples come from the same population. It is the alternative to the two-sample t-test when normality cannot be assumed.

Equality of two means with normal data is the t-test, and comparison of more than two means is analysis of variance (or the Kruskal-Wallis test for ranks).

Answer: D

It is studied through the F-test.

Analysis of variance splits the total variation in data into variation between samples and variation within samples. The ratio of the between-sample variance to the within-sample variance is the F ratio, and the F-test decides whether the sample means differ significantly.

\[ F = \frac{s_{B}^{2}}{s_{W}^{2}} \]

where \(s_{B}^{2}\) is the variance between samples and \(s_{W}^{2}\) the variance within samples.

The chi-square test deals with frequencies and goodness of fit, and the t-test and Z-test compare means directly, not through this split of variance.

Answer: A

The first section of a research paper is the abstract.

The abstract comes immediately after the title and gives a brief summary of the whole paper: the problem, the method, the main findings and the conclusion. It lets readers judge quickly whether the paper is relevant to them, and it is what indexing services display.

The introduction, methodology and analysis follow the abstract in the body of the paper.

Answer: B

The term (1 - B) is called the power of the test, where B (beta) is the probability of a Type II error, which is accepting a false null hypothesis. Its complement 1 - B is the probability of correctly rejecting a false null hypothesis.

The level of the test or its size is the probability of a Type I error, which is denoted by alpha, not by 1 - B. Since the power is the correct name, 'None of the above' is wrong.

Answer: C

The area under the normal curve within \(\mu \pm 3\sigma\) is 0.9973, which is the third value. The standard normal areas are 0.6827 within one standard deviation, 0.9545 within two and 0.9973 within three of the mean.

So 0.6827 is the area for \(\mu \pm \sigma\) and 0.9545 is for \(\mu \pm 2\sigma\). The value 1.0000 is the total area under the whole curve, which is approached only as the limits go to infinity and is not reached at three standard deviations.

Answer: C

The sampling distribution of the mean is very close to the standard normal distribution in both cases: when the population is itself normal, and when it is not normal but the sample size is large. The first holds exactly; the second follows from the central limit theorem, which says that the distribution of the sample mean approaches normality as the sample size grows.

Therefore the combined option 'Both (A) and (B)' is correct, and the options that accept only one of the two or neither are incomplete or wrong. The standard normal form is reached by standardising the mean with its mean and standard error.

Answer: B

The coefficient of correlation is 0.80, because the coefficient of determination is the square of the correlation coefficient.

The value 0.40 is half of 0.80 and 0.64 divided by 1.6, which is not a recognised step. The values 0.08 and 0.04 are obtained by moving the decimal point wrongly. Strictly r could be minus 0.80 as well, but only 0.80 is offered.