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Statistics Class 16 3/26/2012.

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Presentation on theme: "Statistics Class 16 3/26/2012."— Presentation transcript:

1 Statistics Class 16 3/26/2012

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12 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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23 Or use Tinterval

24 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?

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

26 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.

27 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

28 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.

29 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.

30 MethodConditions Use z distribution Use t distribution Other method

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32 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?

33 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.

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


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