Here's a transcription of the image:---b) Find a function of \( \overline{Y} \) that is an unbiased estimator of \( \theta \).3) Suppose that the random variable \( Y \) is an observation from a normal distribution with unknown mean \( \mu \) and variance 1. Find a 95% confidence interval for \( \mu \).comment: Use the CI for \( \mu \) when \( \sigma \) is known and \( n = 1 \).4) "Athletes at major colleges graduated, on the whole, at virtually the same rate as other students," according to the NCAA in 1982. Suppose that in a new poll of...---The text contains specific instructions related to statistics, particularly focusing on unbiased estimation and confidence intervals under certain conditions. It also mentions a statement from the NCAA regarding graduation rates.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Please do a, e, and f only
Suppose that Y is a normally distributed random variable. Assuming that the data is randomly sampled, use the following information to determine the sample variance. Show your work. Use three decimal places. • The sample size is 1225 • The upper limit of a 90 percent confidence interval for E [Y ] is 1.194 • The lower limit of a 90 percent confidence interval for E [Y ] is 1.006.
A random sample of n =18 data from a normal distrinution with unknown variance = 25.1 and s=3. 24. a. Find a 98% confidence interval for the population mean. b. Interpret the interval.
Heart rates are determined before and 30 minutes after a Kettleball workout. It can be assumed that heart rates (bpm) are normally distributed. Use the data provided below to test to determine if average heart rates prior to the workout are significantly lower than 30 minutes after a Kettleball workout at the 0.02 level of significance. Let μ₁ = mean before workout. Select the correct Hypotheses: Ho:με 2 με Η: μι = με Η: μη μ₂ O O O Conclusion: before 69 69 65 62 63 61 after 73 75 72 70 68 59 O Fail to Reject Ho ● Reject Ho Test Statistic = p-value = Ho:μd = 0 H₁: Hd ‡0 O [three decimal accuracy] [three decimal accuracy] Ho:μα 20 Ha:Pa 0 O Interpret the conclusion in context: ● There is enough evidence to suggest the mean bpm before a Kettleball workout is lower than 30 minutes after the workout. O There is not enough evidence to suggest the mean bpm before a Kettleball workout is lower than 30 minutes after the workout.
Test the claim below about the mean of the differences for a population of paired data at the level of significance x. Assume the samples are random and dependent, and the populations are normally distributed. Claim: μ ≥0; x = 0.10. Sample statistics: d= -2.4, s = 1.3, n = 19 Identify the null and alternative hypotheses. Choose the correct answer below. OA. Ho: Hd 0 The test statistic is t = (Round to two decimal places as needed.) The P-value is (Round to three decimal places as needed.) Since the P-value is the level of significance, C OB. Ho: Hd>0 Ha: Hd ≤0 O D. Ho: Hd #0 Ha: Hd = 0 OF. Ho: Hd 20 Ha: Hd <0 the null hypothesis. There statistically significant evidence to reject the claim.
The Wilcoxon signed-rank test can be used to perform a hypothesis test for a population median, η, as well as for a population mean, µ. Why is that so?
Let X 1 , … , X n be identically and independently distributed with population mean 9.3 and standard deviation 1.400. Let xbar be the sample mean, xbar = 1 n ∑ i = 1 n X i. Suppose n = 14. What is the mean squared error (MSE) of 0.742*xbar as an estimator for the population mean?
Suppose x has a normal distribution with σ = 9. A random sample of size 36 has sample mean 20. Find a 95% confidence interval for μ.
Construct a 99% confidence interval for u, - H, with the sample statistics for mean cholesterol content of a hamburger from two fast food chains and confidence interval construction formula below. Assume the populations are approximately normal with unequal variances Stats X, = 98 mg, s,= 3.81 mg, n, = 14 x = 65 mg, s, =222 mg, n, =20 Confidence interval when variances are not equal +t. n2 d.f. is the smaller of n, - 1 or n, - 1 Enter the endpoints of the interval
IID Suppose X1, ..., X, N(u, o?). Construct a 95% confidence interval for o? when u is known.

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3) Suppose that the random variable Y is an observation from a normal distribution with unknown mean and variance 1. Find a 95% confidence interval for μ. comment: Use the CI for u when o is known and n = 1. μ