6:02 PM 77 ??- scribd.com S SCRIBD Search What I Can Do Read the following problems carefully. Apply your skills in solving the following cases. 1. A researcher found that the IQ scores of the ALS students in the Division of Quezon Province are normally distributed with a mean of 110 and a standard deviation of 10 . A. How many ALS students are needed to test so that the estimate will not be more than 5 from the population mean with a \( 99 \% \) level of confidence? B. Due to limited contact with ALS students, the researcher tested a small number of ALS students. Explain the effect of this small sample on the estimate of the parameter? 2. A confidence interval estimate has a maximum error of 2.50 . If the distribution of the data where the estimate is obtained is normal with a standard deviation of 9 , A. How many samples are considered in a \( 98 \% \) confidence interval estimate for the mean? B. What must be done to the sample size to reduce the margin of error of the confidence interval estimate? Support your answer. Download AD
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A. To find out how many ALS students are needed to test so that the estimate will not be more than 5 from the population mean with a 99% level of confidence, we need to use the formula for the sample size in a confidence interval estimate for the mean. The formula Show more…
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#7 An IQ test was given to a simple random sample of 85 students at a certain college. The sample mean score was 110.2. Scores on this test are known to have a standard deviation of σ = 20. It is desired to construct a 90% confidence interval for the mean IQ score of students at this college. a. what is the point estimate? b. find the critical value. c. find the standard error. d. find the margin of error. e. construct the 90% confidence interval. f. is it likely that the population mean μ is greater than 100? explain. 9. Find the critical value tα/2 needed to construct a confidence interval of the given level with the given sample size a. level 95%, sample size 23 b. level 90%, sample size 57
Chai S.
1. IQ scores are normally distributed with mean μ = 100 and standard deviation σ = 15. A researcher desired to build a 95% confidence interval on the IQ scores. Find the sample size n that the researcher needs to achieve a minimum error of 2 IQ units. A. 54 B. 216 C. 345 D. 66 2. A 98% confidence interval on the population proportion p is: CI: (0.521, 0.571). Find the correct proportion estimate p̂ and the error of estimate E from the pair of answers (p̂, E) given. A. (0.546, 0.025) B. (0.566, 0.250) C. (0.526, 0.225) D. (0.526, 0.125)
Ajiboye T.
Please see the setting and reference in Problem 11. Independent random samples from two regions (not those cited in Problem 11 ) gave the following phosphorous measurements (in ppm). Assume the distribution of phosphorous is mound-shaped and symmetric for these two regions. (a) Use a calculator with mean and standard deviation keys to verify that $\bar{x}_{1} \approx 1387.3, s_{1} \approx 498.3, \bar{x}_{2} \approx 1039.3,$ and $s_{2} \approx 346.7$ (b) Let $\mu_{1}$ be the population mean for $x_{1}$ and let $\mu_{2}$ be the population mean for $x_{2} .$ Find an $80 \%$ confidence interval for $\mu_{1}-\mu_{2}$ (c) Explain what the confidence interval means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of different signs? At the $80 \%$ level of confidence, is one region more interesting than the other from a geochemical perspective? (d) Which distribution (standard normal or Student's $t$ ) did you use? Why?
Estimation
Estimating $\mu_{1}-\mu_{2}$ and $p_{1}-p_{2}$
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