There can be multiple answers to this question. The probability that a train is behind schedule is 0.3. A new engine with better acceleration is to betried on the route to see if the arrival time can be improved. To test the effectiveness of the engineimprovements, 10 trials along the route are conducted. The train was behind schedule once.a. State the hypothesis to be considered.b. Identify the test statistic and state the null distribution.c. The test is to be conducted at a significance level of 5%. Find the critical region for this test.

Name: There can be multiple answers to this question. The probability that a
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: There can be multiple answers to this question. The probability that a train is behind schedule is 0.3. A new engine with better acceleration is to betried on the route to see if the arrival time can be improved. To test the effectiveness of the engi

Answered: The probability that a train is behind…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Topic Video

Question

There can be multiple answers to this question.

The probability that a train is behind schedule is 0.3. A new engine with better acceleration is to be
tried on the route to see if the arrival time can be improved. To test the effectiveness of the engine
improvements, 10 trials along the route are conducted. The train was behind schedule once.
a. State the hypothesis to be considered.
b. Identify the test statistic and state the null distribution.
c. The test is to be conducted at a significance level of 5%. Find the critical region for this test.

Expert Solution

Step 1

It is given that we are trying a new engine to see if the arrival time can be improved, hence we want to decrease the probability that a train is behind schedule.

Null hypothesis: P = 0.30
Alternative hypothesis: P < 0.30 (Claim)

This hypotheses constitute a one-tailed test and the significance level is 0.05.

Step 2

We will use normal approximation for the sample proportion, hence the normal distribution would be used and the test statistics is z-statistics.

Use the sample data to perform one sample z-test and calculate the standard deviation (S.D) and compute the z-score test statistic (z).

$\begin{array}{rcl} S . D & = & \sqrt{\frac{P (1 - P)}{n}} \\ = & \sqrt{\frac{0.30 (1 - 0.30)}{10}} \\ = & 0.144913767 \\ \approx & 0.1449 \end{array}$

$\begin{array}{rcl} z & = & \frac{\hat{p} - p}{S . D} \\ = & \frac{0.10 - 0.30}{0.1449} \\ = & - 1.38026225 \\ \approx & - 1.38 \end{array}$

Step by step

Solved in 3 steps

Knowledge Booster

$Research Design Formulation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions