hypothesis and conclusion about parks using if-then
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hypothesis and conclusion about parks using if-then
hypothesis and conclusion about parks using if-then
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Hypothesis
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Answer:
Usea sample mean to test a hypothesis about a known population mean in order to determine if the sample drawn belongs to the specified population (or if it belongs to a different population) For example, if the sample has been affected by some treatment, the sample is not from the typical population but from some other population. Example of Research Question: Does my new math program improve math SAT scores? Math SAT scores were obtained from a sample of 36 students who were in a new math program. The average of those 36 scores was 518. Further, math SAT scores for everyone else (i.e. population against which we are performing our test) is normally distributed with mean of 500 and standard deviation of 100. Perform the test at the .05 level of significance. Statistical Hypotheses Statistical hypotheses with a non-directionalalternative: 0::hypAhypHHStatistical hypotheses with directionalalternatives: a) 0::hypAhypHHb) 0::hypAhypHHSampling Distribution The statistic corresponding to is: XThere are three general properties which define the sampling distribution of X: The distribution of Xis normally distributed The mean of the sampling distribution is: XXThe standard deviation of the sampling distribution (also called the standard error of themean) is: nXXwhere:
Xis the population standard deviation of the dependent variable X and nis the number of observations. Hypothesis Testing about a Single MeanAssumptions 1. Independence of observations (through random sampling) 2. scores in the population are normally distributed * 3. population standard deviation (X) is known * The Central Limit Theoremallows us to overlook assumption 2. Recall that the Central Limit Theoremstates that as the sample size increases, the sampling distribution of approach a normal distribution. In this class, we will consider a sample size of 30 or greater to have a corresponding sampling distribution that is adequately approximated by a normal distribution. The Z Statistic Critical Values Note that because a normally distributed random variable, the Linearly Derived Z Statistic will have the following properties: Normally distributed 0Z1ZThus we may use the Standard Normal Table to find the critical values of Z. Some frequently used values from our standard normal distribution table: Follow the 6-step procedure to test the hypothesis. z Area Beyond the Z 1.645 .050 1.96 .025 2.33 .010 2.58 .005 Note: Use these values in Step 3 of the 6-step process.
Step-by-step explanation:
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