HW5

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School

Stony Brook University *

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Course

2010

Subject

Statistics

Date

Feb 20, 2024

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pdf

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Uploaded by LieutenantCrab1951

Name: _____________________________________________ ID#: _______________________________________________ TA: ________________________________________________ 1. a) For 30 randomly selected Rolling Stones concerts, the mean gross earnings is 2.79 million dollars. Assuming a population standard deviation gross earnings of 0.47 million dollars, obtain a 99% confidence interval for the mean gross earnings of all Rolling Stones concerts (in millions). Confidence interval: ( __________________ , __________________ ). b) Which of the following is the correct interpretation for your answer in part (a)? (A) We can be 99% confident that the mean gross earnings for this sample of 30 Rolling Stones concerts lies in the interval (B) We can be 99% confident that the mean gross earnings of all Rolling Stones concerts lies in the interval (C) There is a 99% chance that the mean gross earnings of all Rolling Stones concerts lies in the interval (D) None of the above 2. Starting salaries of 90 college graduates who have taken a statistics course have a mean of $43,993 and a standard deviation of $9,144. Using 99% confidence level, find the following: A. The margin of error E: _______________________________________ B. The confidence interval for the mean μ: ________________ < μ < ________________ 3. Match the confidence level with the confidence interval for μ. _____ 1. x̄ ± 2.575( σ √࠵? ) A. 90% _____ 2. x̄ ± 1.96( σ √࠵? ) B. 95% _____ 3. x̄ ± 1.645( σ √࠵? ) C. 99% 4. The ability of lizards to recognize their predators via tongue flicks can often mean life or death for lizards. Seventeen juvenile common lizards were exposed to the chemical cues of the viper snake. Their responses, in number of tongue flicks per 20 minutes, are presented below. 540, 744, 710, 251, 285, 591, 472, 370, 268, 608, 421, 693, 506, 268, 200, 778, 574 _______ Ga Lee 114541334 Priyota Saha 2.5090 3.0110 B O 2563.87 41429.13 4655687 A

a) Preliminary data analyses indicate that you can reasonably apply the z-interval procedure. Find a 90% confidence interval for the mean number of tongue flicks per 20 minutes for all juvenile common lizards. Assume a population standard deviation of 190.0. Note: The sum of the data is 8279. Confidence interval: ( __________________ , __________________ ). b) Which of the following is the correct interpretation for your answer in part (a)? (A) We can be 90% confident that the mean number of tongue flicks per 20 minutes for all juvenile common lizards lies in the interval (B) We can be 90% confident that the mean number of tongue flicks per 20 minutes for this sample of 17 lizards lies in the interval (C) There is a 90% chance that the mean number of tongue flicks per 20 minutes for all juvenile common lizards lies in the interval (D) None of the above 5. The following random sample was selected from a normal distribution: 5 20 18 3 10 2 6 9 19 13 a) Construct a 90% confidence interval for the population mean μ : ________________ ≤ μ ≤ ________________ b) Construct a 95% confidence interval for the population mean μ : ________________ ≤ μ ≤ ________________ 6. The standard IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of all adults. We wish to find the sample size necessary to estimate the mean IQ score of statistics students. Suppose we want to be 90% confident that our sample mean is within 2 IQ points of the true mean. As sume then that σ = 15 and determine the required sample size. Answer: _________________ 7. Although, in general, you cannot know the sampling distribution of the sample mean exactly, by what distribution can you often approximate it? (A) Reverse J-shaped (B) Normal (C) J-shaped (D) Uniform _______ _______ 411.1955 562.804 A O 6.6044 14.3956 5 6927 15.3073 153 B

8. What effect does the sample size have on the standard deviation of all possible sample means? (A) The sample size has no effect on it (B) It gets larger as the sample size grows (C) It gets smaller as the sample size grows 9. A variable of a population has a mean of μ = 200 and a standard deviation of σ = 28. a) The sampling distribution of the sample mean for samples of size 49 is approximately normally distributed with mean ________________ and standard deviation ________________. b) For part (a) to be true, what assumption did you make about the distribution of the variable under consideration? (A) Normal distribution (B) Uniform distribution (C) No assumption was made c) Is the statement in part (a) still true if the sample size is 16 instead of 49? Why or why not? (A) No, because the distribution of the variable under consideration is not specified. A sample size of at least 30 is needed for part (a) to be true (B) No, the sampling distribution of the sample mean is never normal for sample size less than 30 (C) Yes, the sampling distribution of the sample mean is always normal _______ _______ _______ C O y 200 A 0 A a

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