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CH 7 Video Ticket #1 Homework to Prepare for 7.1 Day 1 Name: Period: Video – Inferring Population Mean from Sample Mean Question of Interest ________________________________________________________________________________ Draw the picture of the population and sample, then fill in the table below. Fill in the empty boxes…any info you don’t get from the video look up in your textbook. Population Sample Proportion p or (some will use π) 𝑝̂ Standard deviation 𝜎 A number that describes a characteristic (ex height) Mean S2 Variance Video –Central Limit Theorem a) What numbers were described as very likely in the probability distribution? b) What numbers were described as impossible to roll in the probability distribution? What were the means of the first three samples? 𝑥1 = ̅̅̅ 𝑥2 = ̅̅̅ 𝑥3 = ̅̅̅ Sampling variability – In this video there were three samples with a sample size of 4. All three samples could have had a different mean, this is sampling variability. The definition from your textbook is Sampling variability: The value of a statistic varies in repeated random sampling. Central Limit Theorem – (State in your own words) As your sample size gets larger the sampling distribution (of the mean, proportion, sum) . . . Sampling Distribution – The sampling distribution of a statistic is the distribution of values taken by the statistic in all possible samples of the same size from the same population. In the video this would be a distribution of the mean for every possible sample with sample size 4. List 6 more possible samples. S5 = {1,1,1,1} S6 = {1,1,1,3} S7 = S8 = S 9= S10 = S11 = S12 = Unbiased Estimator - A statistic used to estimate a parameter is an unbiased estimator if the mean of its sampling distribution is equal to the true value of the parameter being estimated. Video – Sampling Distribution of the Sample Mean Name of the app – First Example: What was the first sample size? Draw the distribution for 10,000 samples. Draw his examples of skew. Draw his examples of kurtosis. What were the second sample sizes? Draw each distribution and explain the demonstration.