A metropolitan transportation authority has set a bus mechanical reliability goal of 3,800 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 3,825 bus miles and a sample standard deviation of 175 bus miles. Complete parts (a) and (b) below. Question content area bottom Part 1 a. Is there evidence that the population mean bus miles is more than 3,800 bus miles? (Use a 0.05 level of significance.) State the null and alternative hypotheses. H0: μ ▼ equals= less than or equals≤ greater than> greater than or equals≥ not equals≠ less than< enter your response here H1: μ ▼ greater than> not equals≠ less than< less than or equals≤ equals= greater than or equals≥ enter your response here (Type integers or decimals.) Part 2 Find the test statistic for this hypothesis test. tSTAT=enter your response here (Round to two decimal places as needed.) Part 3 The critical value(s) for the test statistic is(are) enter your response here. (Round to two decimal places as needed. Use a comma to separate answers as needed.) Part 4 Is there sufficient evidence to reject the null hypothesis using α=0.05? A. Do not reject the null hypothesis. There is insufficient evidence at the 0.05 level of significance that the population mean bus miles is less than 3,800 bus miles. B. Reject the null hypothesis. There is sufficient evidence at the 0.05 level of significance that the population mean bus miles is greater than 3,800 bus miles. C. Do not reject the null hypothesis. There is insufficient evidence at the 0.05 level of significance that the population mean bus miles is greater than 3,800 bus miles.

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 content area bottom

Part 1

a. Is there evidence that the population mean bus miles is more than

3,800

bus miles? (Use a

0.05

level of significance.)

State the null and alternative hypotheses.

H0:

▼

equals=

less than or equals≤

greater than>

greater than or equals≥

not equals≠

less than<

enter your response here

H1:

▼

greater than>

not equals≠

less than<

less than or equals≤

equals=

greater than or equals≥

enter your response here

(Type integers or decimals.)

Part 2

Find the test statistic for this hypothesis test.

tSTAT=enter your response here

(Round to two decimal places as needed.)

Part 3

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

enter your response here.

(Round to two decimal places as needed. Use a comma to separate answers as needed.)

Part 4

Is there sufficient evidence to reject the null hypothesis using

α=0.05?

Do not reject

the null hypothesis. There is

insufficient

evidence at the

0.05

level of significance that the population mean bus miles is less than

3,800

bus miles.

Reject

the null hypothesis. There is

sufficient

evidence at the

0.05

level of significance that the population mean bus miles is greater than

3,800

bus miles.

Do not reject

the null hypothesis. There is

insufficient

evidence at the

0.05

level of significance that the population mean bus miles is greater than

3,800

bus miles.

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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