Statistical Results Statistic Current Model New Model Sample Mean 270.275 267.500 Standard Error 1.3840 1.5648 Standard Deviation 8.7530 9.8969 Sample Size 40 40 Confidence Level (95%) 2.62 3.14 Degrees of freedom 39 39 t = 1.33 Comparisons 1. A two tail hypothesis test was conducted based on the sample studies of 40 current and 40 new golf balls. The testing was performed with a machine designed to hit the ball the same every time. Both samples were tested with the same machine to ensure consistent
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(you can check this value in Uma Sekaran’s book‚ page 433 in fourth edition of the book. Such normal distribution table is generally given at the end of the most of the intermediate level statistics books). This implies that the probability that the sample mean is two standard deviation away from true mean value is about 0.046. 2. Correlation between two datasets. Let {xi}i and {yi}i be two datasets each having n elements. Pearson’s correlation coefficient‚r‚ is given by the following formula:
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greater mean than the second batch? 2. A sample of 8 independent observations provides the following: 3.6 3.9 3.8 4.5 4.9 4.2 4.4 3.8 Can you conclude at 5% level of significance that the mean is below 5? 3. A house cleaning service claims that they can clean a four bedroom house in less than 2 hours. A sample of n = 16 houses is taken and the sample mean is found to be 1.97 hours and the sample standard deviation is found to be 0.1 hours. (i)
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this machine if a random sample of 36 drinks had an average content of 2.25 dl. 2. The heights of a random sample of 50 college students showed a mean of 174.5 centimeters. Assume the standard deviation is 6.9 cm. What can we assert with 98% confidence about the possible size of our error if we estimate the mean height of all college students to be 174.5? 3. How large a sample is needed in #1 above is we wish to be 95% confident that our sample mean will be within 0.3 dl
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become more familiar with the lab equipment. Repeatability measurements were taken on a bolt to get the total length‚ and also measuring the flow rate of a faucet by measuring the amount of time it took to fill a beaker. To ensure a more accurate sample‚ twenty measurements of each section were obtained. For the batch measurement portion of this lab‚ a multi-meter was used to measure the resistance in a pack of ten resistors. Each member measured the resistors twice to allow for more precise statistical
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that the average pulse rate of adults is 70. For a sample of 64 adults‚ the average pulse rate is 71.8. A significance test is done and the p-value is 0.02. What is the most appropriate conclusion based on α of 0.05? A) Conclude that the population average pulse rate is 70. B) Conclude that the population average pulse rate is 71.8. C) Reject the hypothesis that the population average pulse rate is 70. D) Reject the hypothesis that the sample average pulse rate is 70. Feedback: Since the
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set at 0.05. A random check of 172 unpaid balances revealed the sample mean is $407 and the standard deviation of the sample is $38. Should the credit manager conclude that the population mean is greater than $400? Question 2 A machine is set to fill a specially designed bottle with 9.0 grams of vitamins. It is claimed that the mean is less than 9.0 grams. The hypothesis is to be tested at the 0.01 level. A sample revealed these weights (in
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10.89 1.99 (32.82‚ 39.57) C18 30 40.15 10.30 1.88 (36.96‚ 43.35) C19 30 37.34 9.08 1.66 (34.53‚ 40.16) C20 30 39.46 10.65 1.94 (36.16‚ 42.77) C21 30 34.71 9.21 1.68 (31.85‚ 37.57) d) 1 Sample T-Test for Variable C2 n= 30 df= 29 = 36.91 SE= 1.92 α= 1-CC = 1.0.90 = 0.1 e) Apply binomial theorem for x= 16‚ 17‚18‚19‚20 p=0.9 q=0.1 n=20 16 Interval 17 Interval 18 Interval 19 Interval 20 Interval
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more likely to purchase? o What are the preferred colors? 5. Compute the mean of the following sample values: 16.25‚ 12.91‚ and 14.58. 16.25 + 12.91 + 14.58 = 43.74 43.74 / 3 14.58 21. What is sampling error? Sampling error is the estimated error caused by the observation of a sample instead of the entire population. Could the value of the sampling error be zero? Only when the sample is the entire population the sampling
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random sample of 40 bricks from a day’s output had a mean weight of 4.07lb. (i) Find a 99% confidence interval for the mean weight of all bricks produced on that day. (ii) Estimate the smallest sample size required if the error in estimating the population mean weight of all bricks is to be within 0.03lb with 95% confidence. 2. A house cleaning service claims that they can clean a four bedroom house in less than 2 hours. A sample of n = 16 houses is taken and the sample mean is
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