# Stratified sampling essay

The type of drinks sold is an example of a nominally scaled variable as there are no rankings involved between the drinks. For example, each type of drink is equal. Question 1. 2 U. S. Businesses are listed by size: small, medium, and large. Explain why business size is an example of an ordinal scaled variable NAS. Ordinal value variables are variable which are divided into categories with same ranking or order implied on the categories formed. Therefore the business size is an example of the ordinal scale variable because we divide the variable into disgorges These categories being small, medium and large.

Question 1. 3 The time it takes to download a video from the Internet is measured. A. Explain why the download time is a continuous numerical variable NAS. Numerical variables record numbers through observations. As the time taken to download the file produces a number represented by time, the download is a numerical variable. B. Explain why the download time is a ratio scaled variable NAS. The download time is a ratio scaled variable as the time differences involve a true zero point, meaning that they use the same time scale.

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Question 1. 25 Page 27 Suppose that 5,000 sales invoice are separated into four strata. Stratum 1 contains 50 invoices, stratum 2 contains 500 invoices, stratum 3 contains 1 ,OHO invoices, and stratum 4 contains 3,450 invoices. A sample of 500 sales invoices is needed. A. What type of sampling should you do? Why? NAS. A stratified random sampling is suitable for this study. This is because the population of invoices is heterogeneous which results in increase in the arrange of the estimators.

When the population is divided into homogeneous strata and stratified random sampling is adopted a reduction in the variance of the estimators is attained. B. Explain how you would carry out the sampling according to the method stated in (a). NAS. The size Of the population is 50 + 500 + 1 000 + 3450 5000 The size of the sample is 500 The sampling fraction is 500/5000 = 0. 10= 10% From stratum 1, a simple random sample of size 5 (1 0% of 50) is chosen. From stratum 2, a simple random sample of size 50 (10% of 500) is chosen.

From stratum 3, a simple random sample of size 100 (10% of 1000) is chosen. From stratum 4, a simple random sample of size 345 (10% of 3450) is chosen. Thus a stratified random sample of size 5 + 50 + 100 + 345 = 500 is obtained. C. Why is the sampling in (a) not simple random sampling? NAS. In simple random sampling all possible samples of size 500 are given the same probability of being selected. In stratified random sample, this not the case. For example the probability of selecting 500 invoices from stratum 4 is O. Only 345 invoices are selected from stratum 4.