# QAB 105 Quantitative Analysis For Business

## Question:

Quantra Ltd. is an international wholesaler that provides branded products to retailers. Each product comes with a recommended retail value.

The company became aware that many retailers sell products below the recommended retail price.

It was discovered that 79 of the 200 retailers had sold products below their minimum price.

You are required to:

(a) Define random sampling and describe how they can be selected.

(b) Calculate 95% confidence levels for retailers selling below recommended price, and explain why this is.

Consider the following probability distribution for a random variable X:

X -4 0 0 1 2

P(x=X = 1)

Blacktown’s average home value is \$88950.

It is expected that the value of homes located in the immediate vicinity of Blacktown city will be higher.

This theory is tested by randomly selecting 12 homes in the city.

Their median value is \$92460 with a standard deviation of \$5200.

Perform a hypothesis test using a =0.05.

Assume that prices are normally distributed.

Use five steps to solve the problem using the pvalue approach.

A management accountant attempts to establish a cost-output relation for his company.

This data was collected over the past 2 years.

Units of Output (000)

Cost \$ 000

(a) Utilize linear regression analysis to derive the relationship among the variables and interpret your result.

(b) Calculate the strength of the relationships between variables, and then explain the principle of correlation co-efficient.

Number of retailers that sold products below minimum price = 79

A random sample is a subset of a population in which every element has equal chances or probabilities of being selected.

You can create a random sample by giving all retailers a unique number. After that, 200 numbers can randomly be chosen from the entire population using software. This will avoid any bias.

The random sample would consist of retailers that match the number chosen (Hillier (2006)

95% confidence limit for the proportion

The Mean

Z value for 95% confidence interval = 1.96

95% confidence interval [0.327 0.45627]

Distribution of probability

X

The value

Value = \$88950

Sample size n = 12

92460 = Mean Value

Prices are generally distributed.

Degree of freedom = n-1 = 12, -1 = 11,

With t statistics = 2.338, and degree of liberty = 11, the p-value (one-tailed) is calculated as 0.0196. It is evident that p values are lower than significance levels (0.0196 0.05).

Null hypothesis would therefore be rejected and alternative hypotheses would be accepted (Flick (2015)

Accordingly, it is fair to conclude the average price of Blacktown’s Homes is \$88,950.

Independent variable = Units of Output (000′).

Interpretation

Intercept = 21.25

It refers to the cost for each unit of outputs that is zero.

It means that for every unit of increased output, the cost would increase by 0.9615 (Hastie Tibshirani, Friedman, 2011,).

Strong relationship between output units and cost costs

With the CORREL function, you can determine correlation coefficient.

It is evident that the variables are strongly associated with each other based on the correlation coefficient and the scatterplot.

The positive correlation is evident in the scatter plot’s slope and sign.

The correlation coefficient’s magnitude reflects the intensity or linear relationship (Hair and.

References

The introduction to research methodology: An easy guide for beginning researchers, 4th ed. New York: Sage Publications.

Hair, J. F. Wolfinbarger M. Money, A. H. Samouel P., Page M. J.

New York: Routledge.

Hastie T. Tibshirani R. and Friedman J.

The Elements of Statistical Learning. 4th ed. New York: Springer Publications.

Hillier F. (2006). Introduction to Operations Research. New York: McGraw Hill Publications.