Tuesday, Week 10. Announcements:

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1 Tuesday, Week 10 Announcements: Thursday, October 25, 2 nd midterm in class, covering Chapters 6-8 (Confidence intervals). Charissa Mikoski, the TA for our class, will be administering the exam (I will be at a conference). Tasks for Today 1. Collect GH4 and GH5 2. Finish lecturing on Chapter 8. Confidence intervals when σ is known and when σ is not known.

2 Which was harder for you to do. A. GH4 on Chapter 7, sampling distributions of means was harder B. GH5 on Chapter 8, confidence intervals was harder C. Both were very hard D. Both were pretty easy. If you wanted to include the middle 95 percent of a normal distribution, what Z-scores would mark the upper boundary of the middle 95 percent? A B C D

3 Chapter 8 Confidence Intervals Where is mu (the population mean)?

4 Where is mu, µ, the unknown population mean? Based on the phrase Hurlburt told you (in the lectlets) to memorize you say, I, but it is probably within about (a number) s of the sample mean, Xbar. A. 1 B. 2 C. 3 D.???? A. deviations B. standard deviations C. errors D. standard errors E.???????

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7 From Chapter 7: For All Normally Shaped Sampling Distributions of Means: If 95 percent of all the sample means, X- bars, in a normally shaped sampling distribution of means fall within 1.96 standard errors of the population mean, mu, then if I take one large-n sample (e.g., 1000 cases in the sample) and calculate it s mean, X-bar, what is the chance that the unknown population mean, mu, is within 1.96 standard errors of the mean from X-bar? A. 2.5 percent B. 5 percent C percent D. 95 percent E. One cannot answer the question without more information.

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10 Formula when σ, sigma, st. deviation of the population is known Foreshadowing the last part of this lecture: Formula when σ, sigma, st. deviation of the population is NOT known

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12 1. In a normal distribution, the middle 95 percent of values lie between what two values of Z: and. A. 1 and 1 B and 1.96 C. -2 and 2 D. It is impossible to say without knowing the mean and standard deviation. 2. These two values of Z (described in the previous question are symbolized as and called values. A. sigma sub Xbar, standard error B. sigma, standard deviation C. Zsub Xbar, Z D. ZsubCV, critical

13 In the above formula for the confidence interval when sigma (population standard deviation) is known, Represents: A. the unknown population mean B. the sample mean C. the standard deviation of the sample D. the standard deviation of the sampling distr. of means, standard error Represents: A. the unknown population mean B. the sample mean C. the standard deviation of the sample D. the standard deviation of the sampling distr. of means, standard error

14 In the above formula for the confidence interval when sigma (population standard deviation) is known, the value of A. is determined by looking it up in a table. B. is determined by calculating it from the data and/or information given to you. C. Needs to be given to you in the problem D. is the value that you are trying to estimate in the problem. E. I don t know. A. is determined by looking it up in a table. B. is determined by calculating it from the data and/or information given to you. C. Needs to be given to you in the problem D. is the value that you are trying to estimate in the problem. E. I don t know. A. is determined by looking it up in a table. B. is determined by calculating it from the data and/or information given to you. C. Needs to be given to you in the problem D. is the value that you are trying to estimate in the problem. E. I don t know. A. is determined by looking it up in a table. B. is determined by calculating it from the data and/or information given to you. C. Needs to be given to you in the problem D. is the value that you are trying to estimate in the problem. E. I don t know.

15 In the above formula for the confidence interval when sigma (population standard deviation) is known, the following part of the formula: Is best described as: A. the lower limit of the 95 percent confidence interval. B. the upper limit of the 95 percent confidence interval. C. the probability that mu is between the upper and lower limits of the confidence interval. D. I don t know.

16 Student s home Known location 50 (how many) miles Campus location unknown

17 n = 16 Xbar = 102 IQ points Sigma, standard deviation of population of IQ scores = 16. Find lower and upper limit of 95 percent confidence interval Work with a partner and solve.

18 n = 16 Xbar = 102 IQ points Sigma, standard deviation of population of IQ scores = 16. Find lower and upper limit of 95 percent confidence interval

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21 There is a different t-distribution for every different value of n (sample size) The bigger the sample size, the less error there is in estimating sigma from s And the more the t-distribution resembles the normal distribution

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23 In the above formula for a 95 percent confidence interval for when sigma is unknown, the symbol: A. is determined by looking it up in a table. B. is determined by calculating it from the data and/or information given to you. C. Needs to be given to you in the problem D. is the value that you are trying to estimate in the problem. E. I don t know. A. is determined by looking it up in a table. B. is determined by calculating it from the data and/or information given to you. C. Needs to be given to you in the problem D. is the value that you are trying to estimate in the problem. E. I don t know. A. is determined by looking it up in a table. B. is determined by calculating it from the data and/or information given to you. C. Needs to be given to you in the problem D. is the value that you are trying to estimate in the problem. E. I don t know.

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25 Find Critical Value for 95 percent confidence interval when n= 10

26 Find the correct critical value in the table for 95 percent confidence interval when n= 27 A B C D E. I don t know Find the correct critical value in the table for 95 percent confidence interval when n= 71 A B C. some value between 1.98 and 2.00 D. I don t know In this class, if the degrees of freedom you want is not in the table, use the bigger value for the critical value of t (which corresponds to a smaller degrees of freedom).

27 From Homework, low birth weight babies, σ is not known. Find lower limit and upper limit of 95 percent confidence interval. Work with partners, share the table. N =10

28 Need to estimate the standard error first. Don t know this When sigma is unknown, there is a 95% chance that the mean IQ for all low birth weight babies is between and IQ points.