business research management
- 1. Assignment No. 3 Course Name & Code: BUSINESS RESEARCH MANAGEMENT MBA Sem/Year:2 Sem/ 1yr. Batch: 2019-2021 Date of Submission: Submitted To: Submitted By: Faculty Name: MR. AJAY KHURANA Student Name: APNEET SAINI Max. Marks: …………………… Batch: 2019-2021 Marks Obtained: ……………… UID: 19MBA1286 Faculty Signature……………… Date: ………………………. Acknowledgement by the student after viewing the evaluated copy. Student Name: ……………………………. Signature: …….……………… Date: …………………….
- 2. ASSIGNMENT – 3 BUSINESS RESEARCH MANAGEMENT Explain a) Null hypothesis and alternative hypothesis. b) Type I and type II error c) Acceptance region and rejection region d) Define level of significance. e) power of a hypothesis test and its measurement. A. NULL HYPOTHESIS AND ALTERNATIVE HYPOTHESIS. NULL HYPOTHESIS A null hypothesis is a statistical hypothesis in which there is no significant difference exist between the set of variables. It is the original or default statement, with no effect, often represented by H0 (H-zero). It is always the hypothesis that is tested. It denotes the certain value of population parameter such as µ, s, p. A null hypothesis can be rejected, but it cannot be accepted just on the basis of a single test. ALTERNATIVE HYPOTHESIS A statistical hypothesis used in hypothesis testing, which states that there is a significant difference between the set of variables. It is often referred to as the hypothesis other than the null hypothesis, often denoted by H1 (H-one). It is what the researcher seeks to prove in an indirect way, by using the test. It refers to a certain value of sample statistic, e.g., x¯, s, p The acceptance of alternative hypothesis depends on the rejection of the null hypothesis i.e. until and unless null hypothesis is rejected, an alternative hypothesis cannot be accepted.
- 3. B. Type I and type II error In the context of testing of hypotheses, there are basically two types of errors we can make. We may: reject H0 when H0 is true and accept H0 when in fact H0 is not true The former is known as Type I error and the latter as Type II error. In other words, Type I errormeans rejectionofhypothesis which should have been accepted and Type II error means accepting the hypothesis which should have been rejected. Type I error is denoted by α (alpha) known as α error, also called the level of significance of test; and Type II error is denoted by β (beta) known as β error. The probability of Type I error is usually determined in advance and is understood as the level of significance of testing the hypothesis. If type I error is fixed at 5 per cent, it means that there are about 5 chances in 100 that we will reject H0 when H0 is true. We can controlType I error just by fixing it at a lower level. Forinstance, if we fix it at 1 per cent, we will say that the maximum probability of committing Type I error would only be 0.01.
- 4. C. ACCEPTANCEREGION AND REJECTION REGION The acceptance region is “the interval within the sampling distribution of the test statistic that is consistent with the null hypothesis H0 from hypothesis testing.” In more simple terms, let’s say you run a hypothesis test like a z-test. The results of the test come in the form of a z-value, which has a large range of possible values. Within that range of values, some will fall into an interval that suggests the null hypothesis is correct. That interval is the acceptance region. A rejection region (or critical region) is the set of all values of the test statistic that cause us to reject the null hypothesis. If the test statistic falls into the rejection region, we reject the null hypothesis in favor of the alternative hypothesis. If the test statistic falls in the non-rejection region, we say that we do not have evidence to reject the null hypothesis. Rejection and Non-rejection Regions Outcomes that result in the rejection of the null hypothesis lie in what is termed the rejection region. So, when is the outcome, e.g. a sample mean, so far away from the population mean that the null hypothesis is rejected? The critical values are used to divide the means that lead to the rejection of the null hypothesis from those that do not. A Type I error is committed by rejecting a true null hypothesis. A Type II error is committed when a business researcher fails to reject a false null hypothesis.
- 5. D. DEFINE LEVEL OF SIGNIFICANCE. The level of significance is defined as the fixed probability of wrong elimination of null hypothesis when in fact, it is true. The level of significance is stated to be the probability of type I error and is pre-set by the researcher with the outcomes of error. The level of significance is the measurement of the statistical significance. It defines whether the null hypothesis is assumed to be accepted or rejected. It is expected to identify if the result is statistically significant for the null hypothesis to be false or rejected. Level of Significance Symbol The level of significance is denoted by the Greek symbol α (alpha). Therefore, the level of significance is defined as follows: Significance Level = p (type I error) = α The values or the observations are less likely when they are farther than the mean. The results are written as “significant at x%”. Example: The value significant at 5% refers to p-value is less than 0.05 or p < 0.05. Similarly, significant at the 1% means that the p-value is less than 0.01. The level of significance is taken at 0.05 or 5%. When the p-value is low, it means that the recognised values are significantly different from the population value that was hypothesised in the beginning. The p-value is said to be more significant if it is as low as possible. Also, the result would be highly significant if the p-value is very less. But, most generally, p-values smaller than 0.05 are known as significant, since getting a p-value less than 0.05 is quite a less practice. The general interpretation of the p-value based upon the level of significance of 10%: If p > 0.1, then there will be no assumption for the null hypothesis If p > 0.05 and p ≤ 0.1, it means that there will be a low assumption for the null hypothesis. If p > 0.01 and p ≤ 0.05, then there must be a strong assumption about the null hypothesis. If p ≤ 0.01, then a very strong assumption about the null hypothesis is indicated. E. POWER OF A HYPOTHESIS TEST AND ITS MEASUREMENT. The probability of not committing a Type II error is called the power of a hypothesis test. Effect Size To compute the power of the test, one offers an alternative view about the "true" value of the population parameter, assuming that the null hypothesis is false. The effect size is the difference between the true value and the value specified in the null hypothesis.
- 6. Effect size = True value - Hypothesized value Suppose you want to calculate the power of a hypothesis test on a population means when the standard deviation is known. Before calculating the power of a test you need the following: The previously claimed value of in the null hypothesis, The one-sided inequality of the alternative hypothesis (either < or >), for example, The mean of the observed values The population standard deviation The sample size (denoted n) The level of significance MEASUREMENT OF POWER OF A HYPOTHESIS TEST Type I error occurs if we reject the null hypothesis Ho (in favour of alternative hypothesis H1) when the null hypothesis Ho is true. we denote α = p (type I error). Type II error occurs if we fail to reject the null hypothesis Ho when the alternative hypothesis H1 if true. We denote β = p (type II error)