Let X1,...,X25 be a random sample from a normal distribution with unknown mean μμ and known variance σ2=100.A sample x1,…,x25 is collected and the sample mean from this sample is calculated to be x¯=4. Based on this sample, a 95% confidence interval for μμ is?

From the provided information, Variance (σ2) = 100 Confidence level = 95% Mean (x¯) = 4 Sample size…

Answered: Let X1,...,X25 be a random sample from…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.3: Special Probability Density Functions

Problem 30E

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Let X₁,...,X₂₅ be a random sample from a normal distribution with unknown mean μμ and known variance σ²=100.

A sample x₁,…,x₂₅ is collected and the sample mean from this sample is calculated to be x¯=4. Based on this sample, a 95% confidence interval for μμ is?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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Let X1,...,X25 be a random sample from a normal distribution with unknown mean μμ and known variance σ2=100. A sample x1,…,x25 is collected and the sample mean from this sample is calculated to be x¯=4. Based on this sample, a 95% confidence interval for μμ is