STATISTIC ASSIGNMENT

Statistic Assignment

Statistic Assignment

Question 1

When one researcher rejects the hypothesis while other fails to reject the same hypothesis, the three reasons that cause this difference in result are discussed. The first reason is the difference in observations taken by the two researchers. Both the researchers may have gathered entirely different observations based on different questions. The observations of one researcher may be biased while observations of the other researcher may be unbiased. The second reason is that both the researchers have taken different limit value for the probability of p. The researcher who has rejected the hypothesis has taken the p value of 0.05, while the researcher who failed to reject the hypothesis had taken the p value of 0.01. This can cause the difference in the rejection of the hypothesis. If the probability is less than this p value, the null hypothesis can be false, thus the hypothesis is rejected.  The decision is made by the researcher on the basis of this significance value. The difference in this p value can vary the decision of the researcher (Mann, 1995). The third reason for the difference of the hypothesis testing is the different of test used in the analysis. One researcher may have chosen a test which failed to support the given variables.

In this type of situation, the reader should go with the decision of the researcher who has taken lower value of p that is significance value. This testifies the hypothesis with more accuracy and if the hypothesis is rejected than it will actually be false.

Question 2

Types of errors

There are two types of errors that occurs in a hypothesis testing.

Type I error

A type I error occurs when the null hypothesis Ho is rejected by the researcher, when it is true and should not be rejected. The probability of committing a Type I error is called the significance level. The probability of making a type I error is denoted by the letter alpha a.

Type II error

A type II error occurs when the researcher fails to reject the null hypothesis when it is false and should be rejected. The probability of committing a Type II error is called the power of the test. The probability is denoted by the Greek letter ß.

Question 3

a)

In the completely randomized design, the treatments are randomly assigned to a group of experimental units called block or replication. The random block design was used for both, where the experimental units can be grouped in relatively homogeneous block, so that the differences observed between units are primarily due to the treatments.

It considers three sources of variability:

The treatments factor

The block factor

The random error

The main advantage of this design is that it is easy to analyze, extract experimental error variation due to the addition block variation due to treatment. The disadvantage is that there is low number of degrees of freedom for experimental error. If the number of treatments is very high (about 25), it becomes very difficult to get a good grouping of the experimental plots.

The restriction of this design is that each block must ...