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What is evaluated by the chi-square test for goodness of fit?
The chi-square test for goodness of fit evaluates whether the observed frequencies of categorical data match the expected frequencies under a specific hypothesis. It determines if there are significant differences between the observed distribution of data and the distribution expected based on a theoretical model. This test is commonly used to assess how well a sample distribution fits a population distribution or to test if a sample follows a specified distribution.
How much error is expected between the sample mean and population mean?
0. The expected value of the sample mean is the population mean, so the expected value of the difference is 0.
What is hypothesis of difference?
The alternativehypothesis (Ha or H1) describes the population parameters that the sample data represent, if the predicted relationship exists. It is always the hypothesis of difference. That is as opposed to the null hypothesis (H0) that describes the population parameters that the sample data represent if the predicted relationship does not exist. See Basic Statistics of the Behavioral Sciences by Heiman.
What is the difference between the goodness of fit test and the contingency test?
Goodness of fit test is used to test a single population. The null hypothesis will be that the observed frequencies are equal to expected frequencies (based on computed intrinsic values given the extrinsic values). A good example would be comparing observed phenotype frequencies against expected frequencies calculated from the parental genotypes (Simple dominance gives rise to 1:2:1 ratio with two parental heterozygotes). Contingency test is used to see whether or not different populations are associated. The null hypothesis will be that that different populations are independent of one another. A good example would be comparing the effect of different host plants on different populations of insects. (Effect of Host A on Insect population 1, 2, 3; Effect of Host B on Insect population 1, 2, 3; etc)
How do you prove that the sample variance is equal to the population variance?
You cannot prove it because it is not true.The expected value of the sample variance is the population variance but that is not the same as the two measures being the same.
What term best describes a test used to answer a question?
The term that best describes a test used to answer a question is "hypothesis test." In statistics, a hypothesis test is a method for determining whether there is enough evidence to support a specific claim or hypothesis about a population based on sample data. It involves comparing the observed data to what would be expected under the null hypothesis to draw a conclusion.
What value does the null hypothesis make a claim about?
The null hypothesis makes a claim about the absence of an effect or relationship in the population. It assumes that any observed differences or relationships in the data are due to chance. Researchers aim to reject the null hypothesis in favor of an alternative hypothesis to support their research hypothesis.
What is evaluated by the chi-square test for goodness of fit?
The chi-square test for goodness of fit evaluates whether the observed frequencies of categorical data match the expected frequencies under a specific hypothesis. It determines if there are significant differences between the observed distribution of data and the distribution expected based on a theoretical model. This test is commonly used to assess how well a sample distribution fits a population distribution or to test if a sample follows a specified distribution.
If the chi-square is very large what does it mean?
The null hypothesis in a chi-square goodness-of-fit test states that the sample of observed frequencies supports the claim about the expected frequencies. So the bigger the the calculated chi-square value is, the more likely the sample does not conform the expected frequencies, and therefore you would reject the null hypothesis. So the short answer is, REJECT!
How much error is expected between the sample mean and population mean?
0. The expected value of the sample mean is the population mean, so the expected value of the difference is 0.
On average what value is expected for the t statistic when the null hypothesis is true?
When the null hypothesis is true, the expected value for the t statistic is 0. This is because the t statistic is calculated as the difference between the sample mean and the hypothesized population mean, divided by the standard error, and when the null hypothesis is true, these values should be equal, resulting in a t statistic of 0.
What does the chi-square goodness of fit test determine?
The chi-square goodness of fit test determines whether a set of categorical data have an expected value that is similar to the observed value. For example, if you hypothesized that each Zodiac animal sign has the same proportion of people, then you would look at a sample. You would organize that sample into a chart showing how many people fit into which Zodiac animal. This is your observed value. Then you would have another table to express what your expected value is, which is 1/12 of the total sample population (because there are 12 Zodiac animal signs). Your null hypothesis is that each Zodiac animal sign will have 1/12 of the population. Next, you verify that you can use the chi-square test. To use the chi-square test you must verify that all your expected counts are over 5. Afterwards, you need to calculate a special variable notated as x^2. For each animal, you take the ((observed-expected)^2) / expected. Then you add it up. This is your x^2. Afterwards, you find the P-Value by using a chart or a calculator. If your P-Value is small, this means that the sample could not have occurred by chance and as a result, you can reject your null hypothesis. You would have significant evidence to prove that each Zodiac animal contains a different proportion. If your p-value is large, you fail to reject your null hypothesis.
The closer the sample mean is to the population mean?
Your question is a bit difficult to understand. I will rephrase: In hypothesis testing, when the sample mean is close to the assumed mean of the population (null hypotheses), what does that tell you? Answer: For a given sample size n and an alpha value, the closer the calculated mean is to the assumed mean of the population, the higher chance that null hypothesis will not be rejected in favor of the alternative hypothesis.
How do you know in question of hypothesis that there is population SD or sample SD?
da fac?
What is the meaning of null hypthesis being rejected?
You may want to prove that a given statistic of a population has a given value. This is the null hypothesis. For this you take a sample from the population and measure the statistic of the sample. If the result has a small probability of being (say p = .025) if the null hypothesis is correct, then the null hypothesis is rejected (for p = .025) in favor of an alternative hypothesis. This can be simply that the null hypothesis is incorrect.
What is hypothesis of difference?
The alternativehypothesis (Ha or H1) describes the population parameters that the sample data represent, if the predicted relationship exists. It is always the hypothesis of difference. That is as opposed to the null hypothesis (H0) that describes the population parameters that the sample data represent if the predicted relationship does not exist. See Basic Statistics of the Behavioral Sciences by Heiman.
As the sample size increases what does the expected value of M do?
You have not defined M, but I will consider it is a statistic of the sample. For an random sample, the expected value of a statistic, will be a closer approximation to the parameter value of the population as the sample size increases. In more mathematical language, the measures of dispersion (standard deviation or variance) from the calculated statistic are expected to decrease as the sample size increases.
