Complete Business Statistics by Aczel, Amir D, Sounderpandian, Jayavel, By Amir Aczel Complete Business Statistics 8/E with CD by Amir Aczel [Hardcover. Complete Business Statistics. Front Cover. Amir D. Aczel, Jayavel Sounderpandian. McGraw-Hill/Irwin, – Commercial statistics – pages. Aczel-Sounderpandian: Complete Business Statistics Abridged. Part 1: Principles of Economics. Front Cover. McGraw-Hill, – pages.
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Published by Terence Hopkins Modified over 3 years ago. Trial testimony and evidence Sample data This is the assertion we hold to be true until we have sufficient statistical evidence to conclude otherwise.
Mutually exclusive —Only one can be true.
7-1 COMPLETE BUSINESS STATISTICS by AMIR D. ACZEL & JAYAVEL SOUNDERPANDIAN 6 th edition (SIE)
Exhaustive —Together they cover all possibilities, so one or the other must be true. For example H 0: Often represents the status quo situation or an existing belief. Is maintained, or held to be true, until a test leads to its rejection in favor of the alternative hypothesis. The Null Hypothesis, H 0. The value of the test statistic is used in determining whether or not we may reject the null hypothesis. We may have a decision rule that says: H 0 is true H 0 is false There are two possible decisions: Fail to reject H 0 as true Reject H 0 as false There are two possible states of nature: Fail to reject a true H 0 Reject a false H 0 A decision may be incorrect in two ways: A decision may be correct in two ways: A decision may be incorrect in two ways: Errors in Hypothesis Testing.
The p-value is the probability of obtaining a value of the test statistic as extreme as, or more extreme than, the actual value obtained, when the null hypothesis is true.
More detailed discussions about the p-value will be given later in the chapter when examples on hypothesis tests are presented. The relationship between the population mean and the power of the test is called the power function. The power depends on the population standard deviation: The power depends on the sample size used: The power depends on the level of significance of the test: Factors Affecting the Power Function.
Suppose that you want to carry out a hypothesis test of this claim. Set the null and alternative hypotheses: A consumer advocate wants to test the null hypothesis that the average amount filled by the machine into a bottle is at least cc. A random sample of 40 bottles coming out of the machine was selected and the exact content of the selected bottles are recorded. The sample mean was The population standard deviation is known from past experience to be 1. Compute the p-value for this test.
An automatic bottling machine fills cola into two liter cc bottles.
If action is to be taken if a parameter is greater than some value a, then the alternative hypothesis is that the parameter is greater than a, and the test is a right-tailed test. Conversely, H 0 will not be rejected whenever x-bar is greater than x-bar crit. Consider the following null and alternative hypotheses: Tests of hypotheses about population proportions.
Tests of hypotheses about population variances. We will see the three different types of hypothesis tests, namely Tests of hypotheses about population means. The population need not be normal Testing Population Means. The rejection region, also called the critical region, is defined by the critical points. Note that the population mean may be 28 the null hypothesis might be truebut then the observed sample mean, In this instance, the nonrejection region does not include the observed sample mean, and the confidence interval does not include the hypothesized population mean.
Picturing the Nonrejection and Rejection Regions 0. Do not reject H 0 if the sample mean falls within the nonrejection region between the critical points. Reject H 0 if the sample mean falls outside the nonrejection region. Do not reject H 0 if: This means that for calculations using tables, the sample size n and the population proportion p should have been tabulated.
Aczel-Sounderpandian: Complete Business Statistics Abridged. Part 1 – Google Books
For calculations using spreadsheet templates, sample sizes up to are feasible. Cases in which the binomial distribution can be used The binomial distribution can be used whenever zounderpandian are able to calculate the necessary binomial probabilities.
It is tossed 25 times and only 8 Heads are observed. Using the Template with the Binomial Distribution. Using the Template with the Normal Distribution. The degrees of freedom for this chi-square random variable is n — 1.
Since the chi-square table only provides the critical values, it cannot be used to calculate exact p-values. As in the case of the t-tables, only a range of possible values can be inferred. For testing hypotheses about population variances, the test statistic chi-square is: A random sample of 31 golf balls yields a sample variance of 1.
Enter the hypothesized value of 1 in cell D The p-value of 0. It was decided to test the statistical hypothesis that the average performance time of the task using the new algorithm is the same, against the alternative that the average performance time is no longer the same, at the 0.
The average speed of the standard compact system copier is 27 copies per minute. Suppose the company wants to test whether the new copier has the same average speed as its standard compact copier. Thus, when we reject a null hypothesis, we have a high level of confidence in our decision, since we know there is a small probability that we have made an error. A given sample mean will not lead to a rejection of a null hypothesis unless it lies in outside the nonrejection region of the test.
That is, the nonrejection region includes all sample means that are not significantly different, in a statistical sense, from the hypothesized mean. The rejection regions, in turn, define the values of sample means that are significantly different, in a statistical sense, from the hypothesized mean. The analyst gathered a random sample of accounts of foreign investors in London and found that were owned by U. Suppose that the upper allowable limit on the emission of vinyl chloride is set at an average of 55 ppm within a range of two miles around the plant emitting this chemical.
To check compliance with this rule, the EPA collects a random sample of readings at different times and dates within the two-mile range around the plant. The findings are that the sample average concentration is 60 ppm and the sample standard deviation is 20 ppm.
Is there evidence to conclude that the plant in question is violating the law? The consumer group wants, therefore, to test the hypothesis that the average net weight of the product in question is 12 oz.
A random sample of packages of the food product is collected, and it is found that the average net weight in the sample is Given these findings, is there evidence the manufacturer is underfilling the packages?
A random sample of 21 floodlight elements is chosen and shows that the sample average is The management of a hotel that was denied acceptance to the association wanted to prove that the standards are not as stringent as claimed and that, in fact, the proportion of all hotels in the United States that would qualify is higher than 0.
The management hired an independent research agency, which visited a random sample of hotels nationwide and found that 7 of them satisfied the exact standards set by the association.
Is there evidence to conclude that the population proportion of all hotels in the country satisfying the standards set by the Small Luxury hotels Association is greater than 0.
Complete Business Statistics – Amir D. Aczel, Jayavel Sounderpandian – Google Books
When the p-value is between 0. When the p-value is greater than 0. When the p-value is smaller than 0. Two-Tailed Tests 0. Com;lete a right-tailed test, the p-value is the area to the right of the test statistic if the test statistic is positive. In a left-tailed test, the p-value is the area to the left of the test statistic if the test statistic is negative.
In a two-tailed test, the p-value is twice the area to the right of a positive test statistic or to the left of a negative test statistic.
You can use the different templates that come with the text to investigate these concepts. Similar analysis can be done when testing for a population proportion. Similar analysis can be done when testing a population proportion.
Chapter 12 Tests of Comlpete Means Chap Business Statistics: Chap Chapter 9 Fundamentals of Hypothesis Testing: Chapter Hypothesis Tests Regarding a Parameter My presentations Profile Feedback Log out. Auth with social network: Registration Forgot your password?
OK Chapter 9 Hypothesis Testing.