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An auto maker is interested in information about how long transmissions last. A sample of transmissions are run constantly and the number of miles before the transmission fails is recorded. The auto maker claims that the transmissions can run constantly for over 150,000 miles before failure. The results of the sample are given below. Miles (1000s of miles) Mean Variance Observations Hypothesized Mean 150.7 4.661 46 n = Ex: 5 150 45 df t Stat 2.185 P(T<=t) one-tail 0.017 t Critical one-tail 1.679 P(T<=t) two-tail 0.034 t Critical two-tail 2.014 Confidence Level(95.0%) 0.641 Degrees of freedom = Ex: 5 -3 x -2 -1 Ex: 1.2 s Ex: 1.234 0 2 P= Ex: 1.234 3 Ex: 1.234

An auto maker is interested in information about how long transmissions last. A sample of transmissions are run constantly and the number of miles before the transmission fails is recorded. The auto maker claims that the transmissions can run constantly for over 150,000 miles before failure. The results of the sample are given below. Miles (1000s of miles) Mean Variance Observations Hypothesized Mean 150.7 4.661 46 n = Ex: 5 150 45 df t Stat 2.185 P(T<=t) one-tail 0.017 t Critical one-tail 1.679 P(T<=t) two-tail 0.034 t Critical two-tail 2.014 Confidence Level(95.0%) 0.641 Degrees of freedom = Ex: 5 -3 x -2 -1 Ex: 1.2 s Ex: 1.234 0 2 P= Ex: 1.234 3 Ex: 1.234

MATLAB: An Introduction with Applications
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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An auto maker is interested in information about how long transmissions last. A sample of transmissions are run constantly, and the number of miles before the transmission fails is recorded. The auto maker claims that the transmissions can run constantly for over 150,000 miles before failure. The results of the sample are given below. **Table: Miles (1000s of miles)** - **Mean**: 150.7 - **Variance**: 4.661 - **Observations**: 46 - **Hypothesized Mean**: 150 - **Degrees of freedom (df)**: 45 - **t Stat**: 2.185 - **P(T < t) one-tail**: 0.017 - **t Critical one-tail**: 1.679 - **P(T < t) two-tail**: 0.034 - **t Critical two-tail**: 2.014 - **Confidence Level (95.0%)**: 0.641 **Graph:** The graph shown is a bell-shaped curve representing the t-distribution. The curve peaks around the hypothesized mean and extends symmetrically on both sides. The t-value is marked on the x-axis, providing a visual representation of the sample's t statistic in relation to the distribution. The shaded area under the curve corresponds to the p-value. **Formulas:** - **Sample Size (n)**: \( n = \text{Ex: 5} \) - **Mean (\( \bar{x} \))**: \( \bar{x} = \text{Ex: 1.2} \) - **Degrees of freedom (df)**: \( \text{df} = \text{Ex: 5} \) - **Standard Deviation (s)**: \( s = \text{Ex: 1.234} \) - **p-value (p)**: \( p = \text{Ex: 1.234} \) - **t-value (t)**: \( t = \text{Ex: 1.234} \) This data can aid in determining if there is statistical support for the auto maker's claim about transmission longevity.
Transcribed Image Text:An auto maker is interested in information about how long transmissions last. A sample of transmissions are run constantly, and the number of miles before the transmission fails is recorded. The auto maker claims that the transmissions can run constantly for over 150,000 miles before failure. The results of the sample are given below. **Table: Miles (1000s of miles)** - **Mean**: 150.7 - **Variance**: 4.661 - **Observations**: 46 - **Hypothesized Mean**: 150 - **Degrees of freedom (df)**: 45 - **t Stat**: 2.185 - **P(T < t) one-tail**: 0.017 - **t Critical one-tail**: 1.679 - **P(T < t) two-tail**: 0.034 - **t Critical two-tail**: 2.014 - **Confidence Level (95.0%)**: 0.641 **Graph:** The graph shown is a bell-shaped curve representing the t-distribution. The curve peaks around the hypothesized mean and extends symmetrically on both sides. The t-value is marked on the x-axis, providing a visual representation of the sample's t statistic in relation to the distribution. The shaded area under the curve corresponds to the p-value. **Formulas:** - **Sample Size (n)**: \( n = \text{Ex: 5} \) - **Mean (\( \bar{x} \))**: \( \bar{x} = \text{Ex: 1.2} \) - **Degrees of freedom (df)**: \( \text{df} = \text{Ex: 5} \) - **Standard Deviation (s)**: \( s = \text{Ex: 1.234} \) - **p-value (p)**: \( p = \text{Ex: 1.234} \) - **t-value (t)**: \( t = \text{Ex: 1.234} \) This data can aid in determining if there is statistical support for the auto maker's claim about transmission longevity.
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