Please label each part **Tire Longevity Statistical Analysis**A tire manufacturer claims that its deluxe tire models have an average lifespan of at least 50,000 miles before needing replacement. In previous studies, the standard deviation for this type of tire was found to be 8,000 miles. A recent survey was conducted with 32 tire owners, resulting in an average tire lifespan of 46,600 miles and a standard deviation of 9,800 miles. Given a significance level of alpha = 0.05, is this data consistent with the manufacturer's claim?**Parts of the Analysis:****Part (a):** [No information provided]**Part (b):** [No information provided]**Part (c):** [No information provided]**Part (d):** Statistical Distribution Information- Indicate the distribution to be utilized for evaluation. - Formula: $\bar{X} \sim$ (mean, standard deviation)**Part (e):** Test Statistic Calculation- Determine the test statistic. - Use the $z$ distribution if applicable. Enter your results to two decimal places.**Part (f):** [No information provided]**Part (g):** [No information provided]**Part (h):** [No information provided]**Part (i):** Confidence Interval Construction- Develop a 95% confidence interval to estimate the true mean. Include a diagram depicting the scenario.- Annotate the point estimate and both the lower and upper bounds of the confidence interval, adjusting to the nearest whole number.**Graph Description:**- A bell-shaped curve represents the confidence interval.- The middle of the curve is marked "95% C.I.," indicating the range where the true mean is likely to fall.- Areas under the curve outside the marked interval represent the tails or extremities of the considered data distribution.Understanding this statistical analysis will help in determining whether the observed data supports the manufacturer's claim regarding their tire lifespan.

Part (d) It is clear that the sample size is large(greater than 30), and the population standard…

Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your lower and upper bounds to the nearest whole number.)

Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your lower and upper bounds to the nearest whole number.)

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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Concept explainers

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

Question

Please label each part

**Tire Longevity Statistical Analysis**

A tire manufacturer claims that its deluxe tire models have an average lifespan of at least 50,000 miles before needing replacement. In previous studies, the standard deviation for this type of tire was found to be 8,000 miles. A recent survey was conducted with 32 tire owners, resulting in an average tire lifespan of 46,600 miles and a standard deviation of 9,800 miles. Given a significance level of alpha = 0.05, is this data consistent with the manufacturer's claim?

**Parts of the Analysis:**

**Part (a):** [No information provided]

**Part (b):** [No information provided]

**Part (c):** [No information provided]

**Part (d):** Statistical Distribution Information
- Indicate the distribution to be utilized for evaluation.
- Formula: $\bar{X} \sim$ (mean, standard deviation)

**Part (e):** Test Statistic Calculation
- Determine the test statistic.
- Use the $z$ distribution if applicable. Enter your results to two decimal places.

**Part (f):** [No information provided]

**Part (g):** [No information provided]

**Part (h):** [No information provided]

**Part (i):** Confidence Interval Construction
- Develop a 95% confidence interval to estimate the true mean. Include a diagram depicting the scenario.
- Annotate the point estimate and both the lower and upper bounds of the confidence interval, adjusting to the nearest whole number.

**Graph Description:**
- A bell-shaped curve represents the confidence interval.
- The middle of the curve is marked "95% C.I.," indicating the range where the true mean is likely to fall.
- Areas under the curve outside the marked interval represent the tails or extremities of the considered data distribution.

Understanding this statistical analysis will help in determining whether the observed data supports the manufacturer's claim regarding their tire lifespan.

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