![]() ![]() For a random sample $x_1,\ldots,x_N$ the sample mean will then be denoted by $\bar$, as there $x$ is normal rather than Bernoulli. each student either invests or does not).Ĭommonly a measurement of a random variable will be denoted by $x$. 5.3 Regression when X is a Binary Variable.5.2 Confidence Intervals for Regression Coefficients.5.1 Testing Two-Sided Hypotheses Concerning the Slope Coefficient.5 Hypothesis Tests and Confidence Intervals in the Simple Linear Regression Model.4.5 The Sampling Distribution of the OLS Estimator.Assumption 3: Large Outliers are Unlikely. The "phat" question implicitly concerns a binary measurement (true/false, e.g. The "xbar" question concerns temperature, which is a continuous measurement (e.g. Let samples of size n(>0) be obtained from this. The two questions differ in the type of data that they treat. Let xbar be the mean of a random sample of size n 48 from the uniform distribution on the interval (0,2) that is, f(x) 1/2 for 0 < x < 2. Let the mean and standard deviation of the population distribution be and respectively. Here are the meanings of x bar and p hat that were used to solved the first and last question respectively :īoth questions are essentially applications of the Central Limit Theorem, which says (informally) that "the value of a sum over many samples from a common population will tend to a normal distribution as the number of samples becomes large". Now the standard deviation of x-bar, or as I said it was also called the standard error of the mean, is equal to, and. (And yes I know the second example says give the sampling distribution of p-hat, but I want to know if there is a way to tell if it didn't say that.) Thanks and sorry again if this is a bad question. ![]() So yet again I'm just asking if there is a way to tell if I need to use the equations for xbar or for phat when given a mean, standard deviation, and sample size and asked to give a sampling distribution. (Yet again no need to do this just giving context.) Show the sampling distribution of phat, the sample proportion of business students at this university who invest in the stock market. If we consider the first 16 days of July to be a random sample, what are the expected value, standard deviation, and shape of the sampling distribution of the sample mean? (don't answer this question it's just here to show the question in context.) And now the second using the sample distribution of phatĪssume that 30% of all business students at a university invest in the stock market. That is, the probability distribution of the sample mean is: N (, 2 / n ). In statistics, x-bar ( x) is a symbol used to represent the sample mean of a dataset. ![]() Daily high temperatures in July are normally distributed with a mean of 84 degrees and a standard deviation of 8 degrees. I have two examples from my class one requires a sample distribution of phat and the other a sample distribution of xbar First example using the sample distribution of xbarĪamco Heating and Cooling, Inc., advertises that any customer buying an air conditioner during the first 16 days of July will receive a 25 percent discount if the average high temperature for this 16 day period is more than 5 degrees above normal. Whereas the distribution of the population is uniform, the sampling distribution of the mean has a shape approaching the shape of the familiar bell curve. I was wondering if you can tell the difference between when one is needed and when the other is needed by looking at a mean, standard deviation and sample size. ![]() (feel free to correct me.) I have been learning about creating sample distributions of phat and also sample distributions of xbar. The standard deviation of the sampling distribution is symbolized by Sigma-X-bar and is equal to Sigma divided by the square root of n. =\mu =38.I just started my first statistics class and am not majoring in statistics so sorry if this sounds like a beginner question and also sorry if my language is incorrect. ![]()
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