Chapter 1 : Introduction Learning goals ❖ What is meant by Statistics ❖ What is meant by Descriptive Statistics and Inferential Statistics ❖ Difference between Parameter & Statistic ❖ Types of Statistical Inferences What is meant by Statistics ? Statistics is the science of collecting‚ organizing‚ presenting‚ analyzing‚ and interpreting numerical data to assist in making more effective decisions. Types of Statistics Descriptive Statistics : • Methods of organizing‚ summarizing
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AND 95% AND 99% OF THE NORMAL CURVE STATISTICAL TECHNIQUE IN REVIEW Mean (X) is a measure of central tendency and is the sum of the raw scores divided by the number of scores being summed. Standard deviation (SD) is calculated to measure dispersion or the spread of scores from the mean (Burns & Grove‚ 2007). The larger the value of the standard deviation for study variables‚ the greater the dispersion or variability of the scores for the variable in a distribution. (See Exercise 16 for a
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Standard deviation is the square root of the variance (Gravetter & Wallnau‚ 2013). It uses the mean of the distribution as a reference point and measures variability by considering the distance of each score from the mean. It is important to know the standard deviation for a given sample because it gives a measure of the standard‚ or average‚ range from the mean‚ and specifies if the scores are grouped closely around the mean or are widely scattered (Gravetter & Wallnau‚ 2013). The standard deviation
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population. Furthermore‚ all of the samples will follow an approximate normal distribution pattern‚ with all variances being approximately equal to the variance of the population divided by each sample’s size. Using the central limit theorem allows you to find probabilities for each of these sample statistics without having to sample a lot. The central limit theorem is a major probability theorem that tells you what sampling distribution is used for many different statistics‚ including the sample total
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and Y vary together. SPxy = ∑ [(X - Mx) * (Y - My)] r = SPxy / sqrt (SSx * SSy). SSx‚ SSy are measures of the degree to which X and Y vary independently. Z score formula: r = ∑ (Zx * Zy) / N Covariance = SP / N Assumptions for r: 1) normal distribution of X and Y - check histograms 2) linear relationship between X and Y - check scatterplots 3) homoscedasticity - vertical distance between scatterplot dots and regression line; indicates level of prediction error (aka “residual”) Measurement
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Q. Explain the term Sampling distribution The term sampling distribution refers to a frequency or probability distribution of the sample statistic obtained from all the possible samples of size n taken at random from a given population. The sample mean (x) shows the average value calculated from measurements of a sample. Its main characteristics are: 1. The average of all sample means should equal to the true population mean (µ) 2. The standard deviation shows dispersion
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................................ 6 2.3 Location Statistics (measures of central tendency) ...................................... 7 2.4 Dispersion Statistics (measures of variability) ............................................... 8 FREQUENCY DISTRIBUTIONS ........................................... 10 3.1 Frequency Measures.............................................................................................. 10 3.2 Histogram ..............................................................
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A ’bell curve ’ is perfectly symmetrical with respect to a vertical line through its peak and is sometimes called a "Gauss curve" or a "normal curve". The second shape a scatter diagram may have is anything but a normal curve as in the next drawing: We can do a lot of good statistics with the normal curve‚ but virtually none with any other curve. Let us assume that we have recorded the 1000 ages and computed the mean and standard
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1. Cu = 24-11 = $13 Co = 11-7 = $4 Critical ratio = 13/(13+4) = 0.7647 μ = 30‚000 σ = 10‚000 Using normal distribution function (=norminv(0.7647‚30000‚10000))‚ the optimum order quantity is 37‚216 jerseys to maximize profit. 2. Quantity = 32‚000 First‚ we normalize the order quantity to find the z-statistic z=Q-μσ=32‚000-25‚00010‚000=0.7 We then look up the standard normal loss function. The expected lost sale is given by. Lz=0.1429 Therefore‚ the expected lost sales = 10‚000 *
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the correct answer. 1. When s is used to estimate (‚ the margin of error is computed by using a. normal distribution b. t distribution c. the mean of the sample d. the mean of the population Answer: b 2. As the number of degrees of freedom for a t distribution increases‚ the difference between the t distribution and the standard normal distribution a. becomes larger b. becomes smaller c. stays the same d. None of these alternatives is correct.
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