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In an essay of 250-500 words, thoroughly address the following items and respond to the related questions:
1.Define the term standard deviation. Why is it important to know the standard deviation for a given sample? What do researchers learn about a normal distribution from knowledge of the standard deviation? A sample of n=20 has a mean of M = 40. If the standard deviation is s=5, would a score of X= 55 be considered an extreme value? Why or why not?
2.Hypothesis testing allows researchers to use sample data, taken from a larger population, to draw inferences (i.e., conclusions) about the population from which the sample came. Hypothesis testing is one of the most commonly used inferential procedures. Define and thoroughly explain the terms null hypothesis and alternative hypothesis. How are they used in hypothesis testing?
3. Define the term standard error. Why is the standard error important in research using sample distributions? Consider the following scenario: A random sample obtained from a population has a mean of µ=100 and a standard deviation of σ = 20. The error between the sample mean and the population mean for a sample of n = 16 is 5 points and the error between a sample men and population mean for a sample of n = 100 is 2 points. Explain the difference in the standard error for the two samples.
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It is computed by the average distance from the average or average of all the averages for multiple sets of data. It is important because it measures the variability in the set of data. It helps in finding how close the values of data set are to the mean. We compute the z-score to find whether it is an extreme value. The Z-score = (55 – 40)/5 = 3. Since the z-score lies outside the two standard deviations from the mean, therefore it is considered to be an extreme value. Standard deviation is a measure of dispersion. It is computed by the average distance from the average or average of all the averages for multiple sets of data. We compute the z-score to find whether it is an extreme value. The Z-score = (55 – 40)/5 = 3. Since the z-score lies outside the two standard deviations from the mean, therefore it is considered to be an extreme value. The traditional hypothesis testing requires setting up two competing statements known as null hypothesis and alternative hypothesis. They are mutually exclusive and exhaustive. Null hypothesis Ho: The finding occurred by chance. It represents theory either because it is believed to be true or because it is used as a basis of argument, but not proved. Alternative Hypothesis H1: The finding did not occur by chance. It is a statement of what a hypothesis test is set to be established. They are used in hypothesis testing when the question is interested in simplified into two competing claims between there are two choices, the null hypothesis (Ho) against the alternative hypothesis (Ha). These two competing claims are not treated on equal basis; special consideration is given to the null hypothesis. Standard error is the standard deviation divided by the square root of sample size. It is known as the standard deviation of sampling distribution. It measures how much sample statistic varies from sample to sample. It is important because how much sampling fluctuate with the statistics. The inferential statistics involves confidence and significance testing which are based on the standard errors. The standard error depends on the sample size. Larger the sample size, smaller the standard error. The difference between the two samples is as the sample size increases, the standard error decreases because standard error and sample size are inversely related.