solution2 - 1. C. The formula for the confidence interval...

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1. C. The formula for the confidence interval for a population mean is: x t s n , which was based on the sample Mean. So, “ x ” is guaranteed to be in the interval you form. 2. D. Use the rule : p-value <alpha, reject H 0 . The P-value is greater than the significance level (=.10), so we can conclude the data do not provide sufficient evidence to reject the null hypothesis (H 0 ). Fail to reject H 0 . 3. A. The formula for confidence interval is: x t s n where (t s n ) is the margin of error. Other things being equal, the margin of error of a confidence interval increases as the sample size n decreases. So, when the sample size decreases, the length of the confidence interval will become bigger. 4. B. Similar to the previous question. Other things being equal, the margin of error of a confidence interval decreases as the confidence level (t -score) decreases. So, the length of the confidence interval will become smaller when the confidence level decreases. 5. D. From the results of the previous two questions, we know that when the sample size increases, the confidence interval will be smaller. However, it will become bigger as the confidence level increases. Therefore, we cannot conclude how the confidence interval will be in this question, since we don’t have enough information to determine whether the change in sample size or the confidence level is more influential here. 6. C. 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. The mean of the sampling distribution of x is  the population mean. 7. A. Since the P-value is a probability, so it must be between 0 and 1. 8. B. For 95% confidence, z = 1.96. For a margin of error of 0.5, we have n= 2 * zs m    = 2 1.96*10 0.5 =1536.6. So, the sample size should be 1537. (Always round up to the next higher whole number when finding n). 9. C. Take the 93% and change it to a decimal (0.93). Take 1 - .93 = 0.07 (this is the area in the tails). Divide this number in half (0.035.) Look in the middle of the table for the entry 0.035. This corresponds to - z=-1.81. Thus, z=1.81. In short look up (1-0.93)/2=.035 in the middle of the table and z is the absolute value of the z-score.
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10. D. The sampling distribution of x is the distribution of values taken by x in all possible samples of the same size from the same population. 11. B. Because we infer conclusions about the population from data on selected Individuals (all sample). 12. a. F. In a very large number of samples, 95% of the confidence intervals would contain  the population mean. If the endpoints of the CI are given, use the term confidence, not probability. b. T. The definition of confidence interval. We are 95% confidence that the unknown lies between (1.15, 4.20). c. F. The center of each interval is at x , and therefore varies from sample to sample. So, when 100 intervals calculated the same way, we can expect 100 of them to capture their own sample mean. Not only 95% of them.
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This note was uploaded on 11/11/2010 for the course STA 2023 taught by Professor Ripol during the Fall '08 term at University of Florida.

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solution2 - 1. C. The formula for the confidence interval...

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