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Statistics Class 16 3/26/2012

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How many integrated circuits must be randomly selected and tested for time to failure in order to estimate the mean time to failure? We want a 95% confidence that the sample mean is within 2 hr. of the population mean, and the population standard deviation is known to be 18.6 hours.

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Or use Tinterval

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In a test of the Atkins weight loss program, 40 individuals participated in a randomized trial with overweight adults. After 12 months, the mean weight loss was found to be 2.1 lb, with a standard deviation of 4.8 lb What is the best point estimate of the mean weight loss of all overweight adults who follow the Atkins program? Construct a 99% confidence interval estimate of the mean weight loss for all such subjects. Does the Atkins program appear to be effective? Is it practical?

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Important properties of the t distribution. 1.The Student t distribution is different for different sample sizes.

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Important properties of the t distribution. 1.The Student t distribution is different for different sample sizes. 2.The Student t distribution has the same general symmetric bell shape as the standard normal distribution, but reflects the greater variability that is expected with small samples.

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Important properties of the t distribution. 1.The Student t distribution is different for different sample sizes. 2.The Student t distribution has the same general symmetric bell shape as the standard normal distribution, but reflects the greater variability that is expected with small samples. 3.The Student t distribution has a mean of t=0

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Important properties of the t distribution. 1.The Student t distribution is different for different sample sizes. 2.The Student t distribution has the same general symmetric bell shape as the standard normal distribution, but reflects the greater variability that is expected with small samples. 3.The Student t distribution has a mean of t=0 4.The standard deviation of a t distribution varies with the sample size but is always larger than 1.

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Important properties of the t distribution. 1.The Student t distribution is different for different sample sizes. 2.The Student t distribution has the same general symmetric bell shape as the standard normal distribution, but reflects the greater variability that is expected with small samples. 3.The Student t distribution has a mean of t=0 4.The standard deviation of a t distribution varies with the sample size but is always larger than 1. 5.As n gets large the t distribution becomes more like the standard normal distribution.

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MethodConditions Use z distribution Use t distribution Other method

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Listed below are 12 lengths (in minutes) of randomly selected movies Construct a 99% confidence interval estimate of the mean length of all movies. Assuming that it takes 30 min to empty a theater after a movie, clean it, allow time for the next audience to enter, and show previews, what is the minimum time that a theater manager should plan between start times of movies, assuming that this time will be sufficient for typical movies?

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Quiz 13 When Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 428 green peas and 152 yellow peas. a.Find a 95% confidence interval estimate of the percentage of yellow peas. b.Based on his theory of genetics, Mendel expected that 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is not 25%, do the results contradict Mendel’s Theory? Why or why not.

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Homework!! 7-3: 1-9 odd, 13,15, odd. 7-4: 1-12, odd.

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