other Non-symmetrical distributions are said to be “skewed” a) Skewed to the right (Positively skewed) Mode < Median < Mean b) Skewed to the left (Negatively skewed) Mode > Median > Mean c) Symmetric Distribution Mode = Median = Mean Measures of Central Tendency: The Mean‚ Mode and Median The mean is the average of scores: Population mean: μ = Σ xi/N Sample mean: x = Σ xi/n The mode is the value that has the highest frequency The median is the middle value of data ordered from
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components produced by the manufacturer have a mean diameter of 0.75 inch with a standard deviation of 0.004 inch. The quality-control inspector takes a random sample of 30 components once each week and calculates the mean diameter of these components. If the mean is either less than 0.748 inch or greater than 0.752 inch‚ the inspector concludes that the machine needs an adjustment. (a) Describe the sampling distribution of the sample mean diameter for a random sample of 30 such components
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Thermal comfort indices The calculations of the PMV (predicted mean vote) and PPD (predicted percent of dissatisfied people) were done by using the CBE Thermal Comfort Tool of the University of California Berkeley that has been proposed based on ASHRAE Standard 55-2013 (Tyler‚ et al.‚ 2017). The result obtained after calculating PMV index for (H1) is varies between 1.63 to 2.1with the mean value of 1.99‚ and the 80% satisfaction falls within the range of [-1.99< PMV< +1.99]. By equating to ASHRAE
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Chapter 9 Hypothesis Testing Case Problem 1: Quality Associates‚ Inc. 1. The hypothesis testing results are shown below: Sample 1 Sample 2 Sample 3 Sample 4 Sample Size 30 30 30 30 Mean 11.959 12.029 11.889 12.081 Standard Deviation 0.220 0.220 0.207 0.206 Level of Significance (alpha) 0.010 0.010 0.010 0.010 Critical Value (lower tail) -2.576 -2.576 -2.576 -2.576 Critical Value (upper tail) 2.576 2.576 2.576 2.576 Hypothesized value 12 12 12 12 Standard Error 0.040
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deviation shows how much variation or "dispersion" exists from the average (mean‚ or expected value). A low standard deviation indicates that the data points tend to be very close to the mean‚ whereas high standard deviation indicates that the data points are spread out over a large range of values 2.3 Definition of Coefficient of Varience The coefficient of variation represents the ratio of the standard deviation to the mean‚ and it is a useful statistic for comparing the degree of variation from
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deviation of 25 and computed the sample mean to be 100. a.Use an interval estimate to estimate the population mean with 90% confidence.[mu-1.64*SD/√n‚mu+1.64*SD/√n] [100-1.64*25/√50‚100+1.64*25/√50][94.2017‚105.7983]-90% Confidence b.95% confidence. [mu-1.96*SD/√n‚mu+1.96*SD/√n] [100-1.96*25/√50‚100+1.96*25/√50][93.0704‚106.9296]-95% Confidence c.99% confidence. [mu-2.57*SD/√n‚mu+2.57*SD/√n] [100-2.57*25/√50‚100+2.57*25/√50][90.9137‚109.0863]-99% Confidence The mean of a sample of size n=35 was calculated
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A hypothesis is a claim Population mean The mean monthly cell phone bill in this city is μ = $42 Population proportion Example: The proportion of adults in this city with cell phones is π = 0.68 States the claim or assertion to be tested Is always about a population parameter‚ not about a sample statistic Is the opposite of the null hypothesis e.g.‚ The average diameter of a manufactured bolt is not equal to 30mm ( H1: μ ≠ 30 ) Challenges the status quo Alternative never contains
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(iii) Find the mean‚ median‚ range and standard deviation for the 1990 returns. Annual Returns % (1990) Mean 12.91865979 Median 11.38 Standard Deviation 9.297513067 Range 75.01 (iv) Repeat part (iii) for the 1998 returns. Annual Returns % (1998) Mean 6.355463918 Median 5.4 Standard Deviation 5.170830853 Range 42.76 (v) Which was the better year for investors? • 1990 was the better year for investors in regards to annual returns being consistent with the mean of 12.9% compare to
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measurements from a population having a mean equal to 20 and a standard deviation equal to 4. A. Describe the shape of the sampling distribution of the sample mean x. Do we need to make any assumptions about the shape of the population? Why or why not? ------------------------------------------------- This would be a normally distributed bell shaped curve. We do not need to make any assumptions because the sample size is at least 30. B. Find the mean and the standard deviation of the sampling
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Statistics For Management 1. Introduction 2. Statistical Survey 3. Classification‚ Tabulation & Presentation of data 4. Measures used to summarise data 5. Probabilities 6. Theoretical Distributions 7. Sampling & Sampling Distributions 8. Estimation 9. Testing of Hypothesis in case of large & small samples 10. Chi-Square 11. F-Distribution and Analysis of variance (ANOVA) 12. Simple correlation and Regression 13. Business Forecasting 14. Time Series Analysis 15 . Index Numbers Indian
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