The speeds of vehicles traveling on a highway are normally distributed with an unknown population mean and standard deviation. A random sample of 11 vehicles has taken in results and a sample mean of 65 mph in a sample standard deviation of 9 mph. Find a 90% confidence interval estimate for the population mean using the students T- distribution. Round final answers to two decimal places. ### Student's t-Distribution Critical Values TableThe table below provides critical values from the Student's t-distribution, commonly used in statistical analyses to determine confidence intervals and hypothesis testing.#### Columns:- **df**: Represents degrees of freedom, which is calculated as the sample size minus 1.- **t0.10**, **t0.05**, **t0.025**, **t0.01**, **t0.005**: Correspond to the critical values at different significance levels (alpha values), where the subscript indicates the tail area in a two-tailed test.#### Data:- **df = 9** - t0.10: 1.383 - t0.05: 1.833 - t0.025: 2.262 - t0.01: 2.821 - t0.005: 3.250- **df = 10** - t0.10: 1.372 - t0.05: 1.812 - t0.025: 2.228 - t0.01: 2.764 - t0.005: 3.169- **df = 11** - t0.10: 1.363 - t0.05: 1.796 - t0.025: 2.201 - t0.01: 2.718 - t0.005: 3.106- **df = 12** - t0.10: 1.356 - t0.05: 1.782 - t0.025: 2.179 - t0.01:

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Description: The speeds of vehicles traveling on a highway are normally distributed with an unknown population mean and standard deviation. A random sample of 11 vehicles has taken in results and a sample mean of 65 mph in a sample standard deviation of 9 mph. Fi

Given : Sample mean = x¯ =65 mph sample standard deviation = σ = 9 mph n = 11 tα2, n-1= t0.102,…

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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The speeds of vehicles traveling on a highway are normally distributed with an unknown population mean and standard deviation. A random sample of 11 vehicles has taken in results and a sample mean of 65 mph in a sample standard deviation of 9 mph. Find a 90% confidence interval estimate for the population mean using the students T- distribution. Round final answers to two decimal places.

### Student's t-Distribution Critical Values Table

The table below provides critical values from the Student's t-distribution, commonly used in statistical analyses to determine confidence intervals and hypothesis testing.

#### Columns:
- **df**: Represents degrees of freedom, which is calculated as the sample size minus 1.
- **t<sub>0.10</sub>**, **t<sub>0.05</sub>**, **t<sub>0.025</sub>**, **t<sub>0.01</sub>**, **t<sub>0.005</sub>**: Correspond to the critical values at different significance levels (alpha values), where the subscript indicates the tail area in a two-tailed test.

#### Data:

- **df = 9**
- t<sub>0.10</sub>: 1.383
- t<sub>0.05</sub>: 1.833
- t<sub>0.025</sub>: 2.262
- t<sub>0.01</sub>: 2.821
- t<sub>0.005</sub>: 3.250

- **df = 10**
- t<sub>0.10</sub>: 1.372
- t<sub>0.05</sub>: 1.812
- t<sub>0.025</sub>: 2.228
- t<sub>0.01</sub>: 2.764
- t<sub>0.005</sub>: 3.169

- **df = 11**
- t<sub>0.10</sub>: 1.363
- t<sub>0.05</sub>: 1.796
- t<sub>0.025</sub>: 2.201
- t<sub>0.01</sub>: 2.718
- t<sub>0.005</sub>: 3.106

- **df = 12**
- t<sub>0.10</sub>: 1.356
- t<sub>0.05</sub>: 1.782
- t<sub>0.025</sub>: 2.179
- t<sub>0.01</sub>:

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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