A metropolitan transportation authority has set a bus mechanical reliability goal of3,900bus miles. Bus mechanical reliability is measured specifically as the number of bus miles between mechanical road calls. Suppose a sample of100buses resulted in a sample mean of3,975bus miles and a sample standard deviation of275bus miles. Complete parts (a) and (b) below. A metropolitan transportation authority has set a bus mechanical reliability goal of 3,900 bus miles. Bus mechanical reliability is measured specifically as the number of bus miles between mechanical road calls. Suppose a sample of 100 buses resulted in a sample mean of 3,975 bus miles and a sample standard deviation of 275 bus miles. Complete parts (a) and (b) below.---**a. Is there evidence that the population mean bus miles is more than 3,900 bus miles? (Use a 0.10 level of significance.)****State the null and alternative hypotheses:**- $ H_0: \mu \square $- $ H_1: \mu \square $*(Type integers or decimals.)***Find the test statistic for this hypothesis test.**- $ t_{\text{STAT}} = \square $ (Round to two decimal places as needed.)**The critical value(s) for the test statistic is(are):**- $\square$ (Round to two decimal places as needed. Use a comma to separate answers as needed.)**Is there sufficient evidence to reject the null hypothesis using $\alpha = 0.10$?**- **A.** Reject the null hypothesis. There is sufficient evidence at the 0.10 level of significance that the population mean bus miles is greater than 3,900 bus miles.- **B.** Do not reject the null hypothesis. There is insufficient evidence at the 0.10 level of significance that the population mean bus miles is greater than 3,900 bus miles.- **C.** Do not reject the null hypothesis. There is insufficient evidence at the 0.10 level of significance that the population mean bus miles is less than 3,900 bus miles.- **D.** Reject the null hypothesis. There is sufficient evidence at the 0.10 level of significance that the population mean bus miles is less than 3,900 bus miles.---**b. Determine the p-value and interpret its meaning.****The p-value is $\square$.***(Round to three decimal places as needed.)***What does the p-value mean given the results of part (a)?**- **A.** The p-value is the probability that the actual mean is greater than 3,975 bus miles.- **B.** The p-value is the probability of getting a sample mean of

Answered: A metropolitan transportation authority…

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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Question

A metropolitan transportation authority has set a bus mechanical reliability goal of

3,900

bus miles. Bus mechanical reliability is measured specifically as the number of bus miles between mechanical road calls. Suppose a sample of

100

buses resulted in a sample mean of

3,975

bus miles and a sample standard deviation of

275

bus miles. Complete parts (a) and (b) below.

A metropolitan transportation authority has set a bus mechanical reliability goal of 3,900 bus miles. Bus mechanical reliability is measured specifically as the number of bus miles between mechanical road calls. Suppose a sample of 100 buses resulted in a sample mean of 3,975 bus miles and a sample standard deviation of 275 bus miles. Complete parts (a) and (b) below.

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**a. Is there evidence that the population mean bus miles is more than 3,900 bus miles? (Use a 0.10 level of significance.)**

**State the null and alternative hypotheses:**

- $ H_0: \mu \square $
- $ H_1: \mu \square $

*(Type integers or decimals.)*

**Find the test statistic for this hypothesis test.**

- $ t_{\text{STAT}} = \square $ (Round to two decimal places as needed.)

**The critical value(s) for the test statistic is(are):**

- $\square$ (Round to two decimal places as needed. Use a comma to separate answers as needed.)

**Is there sufficient evidence to reject the null hypothesis using $\alpha = 0.10$?**

- **A.** Reject the null hypothesis. There is sufficient evidence at the 0.10 level of significance that the population mean bus miles is greater than 3,900 bus miles.
- **B.** Do not reject the null hypothesis. There is insufficient evidence at the 0.10 level of significance that the population mean bus miles is greater than 3,900 bus miles.
- **C.** Do not reject the null hypothesis. There is insufficient evidence at the 0.10 level of significance that the population mean bus miles is less than 3,900 bus miles.
- **D.** Reject the null hypothesis. There is sufficient evidence at the 0.10 level of significance that the population mean bus miles is less than 3,900 bus miles.

---

**b. Determine the p-value and interpret its meaning.**

**The p-value is $\square$.**

*(Round to three decimal places as needed.)*

**What does the p-value mean given the results of part (a)?**

- **A.** The p-value is the probability that the actual mean is greater than 3,975 bus miles.
- **B.** The p-value is the probability of getting a sample mean of

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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Let $mu$ denote the population mean bus miles.

The claim of the test is that the population's mean bus miles is more than 3,900 bus miles.