Explanation Given info: The claim is that the proportion is at least 40%. The sample size is n = 50 and p = 0.6 . Calculation: Null hypothesis: Null hypothesis is a statement about population parameter, its value is equal to the claim value, which is denoted by H 0 . The population parameter can be mean, standard deviation, proportion, variance, and so forth. The possible symbols used in the null hypothesis would be ≤ , ≥ , or =. Alternative hypothesis: It is complementary to the null hypothesis. That is, it differs from the null hypothesis. The possible symbols used in the alternative hypothesis would be <,>, or ≠. It is denoted by H a . Here, the claim is that the proportion is at least 40%. This can be written as p ≥ 0.40 . The complement of the claim is, p < 0.40 . State the null and alternative hypotheses: Null hypothesis: H 0 : p ≥ 0.40 Alternative hypothesis: H a : p < 0.40 Run the simulation so that at least 1,000 hypothesis tests are run: Software Procedure: Consider the level of significance as 0.05. Step-by-step procedure to obtain the proportion is given below: Click Hypothesis tests for a proportion . Select Normal as distribution. Enter the sample size as 50 , True p: as 0.6 and Null p: as 0.40 . Click Update Applet . Choose less than symbol in alternative . Enter the level of significance as 0.05 . Select 1,000 tests Output obtained from Applet is given below: From the output, the proportion is 0. Consider the level of significance as 0

Elementary Statistics Plus MyLab Statistics with Pearson eText -- Access Card Package (7th Edition) (What's New in Statistics)

7th Edition

ISBN: 9780134684901

Author: Ron Larson, Betsy Farber

Publisher: PEARSON

See similar textbooks

Concept explainers

2-Proportion Test

In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.

Videos

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 7.4, Problem 2A

To determine

To find: The null and alternative hypotheses.

To run: The simulation so that at least 1,000 hypothesis tests are run.

To compare: The proportion of null hypothesis rejections for the 0.05 level and the 0.01 level.

To perform: The hypotheses test for each level.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 7.4, Problem 1A

Chapter 7.5, Problem 1TY

Students have asked these similar questions

ons 12. A sociologist hypothesizes that the crime rate is higher in areas with higher poverty rate and lower median income. She col- lects data on the crime rate (crimes per 100,000 residents), the poverty rate (in %), and the median income (in $1,000s) from 41 New England cities. A portion of the regression results is shown in the following table. Standard Coefficients error t stat p-value Intercept -301.62 549.71 -0.55 0.5864 Poverty 53.16 14.22 3.74 0.0006 Income 4.95 8.26 0.60 0.5526 a. b. Are the signs as expected on the slope coefficients? Predict the crime rate in an area with a poverty rate of 20% and a median income of $50,000. 3. Using data from 50 work

2. The owner of several used-car dealerships believes that the selling price of a used car can best be predicted using the car's age. He uses data on the recent selling price (in $) and age of 20 used sedans to estimate Price = Po + B₁Age + ε. A portion of the regression results is shown in the accompanying table. Standard Coefficients Intercept 21187.94 Error 733.42 t Stat p-value 28.89 1.56E-16 Age -1208.25 128.95 -9.37 2.41E-08 a. What is the estimate for B₁? Interpret this value. b. What is the sample regression equation? C. Predict the selling price of a 5-year-old sedan.

ian income of $50,000. erty rate of 13. Using data from 50 workers, a researcher estimates Wage = Bo+B,Education + B₂Experience + B3Age+e, where Wage is the hourly wage rate and Education, Experience, and Age are the years of higher education, the years of experience, and the age of the worker, respectively. A portion of the regression results is shown in the following table. ni ogolloo bash 1 Standard Coefficients error t stat p-value Intercept 7.87 4.09 1.93 0.0603 Education 1.44 0.34 4.24 0.0001 Experience 0.45 0.14 3.16 0.0028 Age -0.01 0.08 -0.14 0.8920 a. Interpret the estimated coefficients for Education and Experience. b. Predict the hourly wage rate for a 30-year-old worker with four years of higher education and three years of experience.

Chapter 7 Solutions

Elementary Statistics Plus MyLab Statistics with Pearson eText -- Access Card Package (7th Edition) (What's New in Statistics)

Ch. 7.1 - Write each claim as a mathematical statement....Ch. 7.1 - A company specializing in parachute assembly...Ch. 7.1 - For each claim, state H0 and Ha in words and in...Ch. 7.1 - You perform a hypothesis test for each claim. How...Ch. 7.1 - 1. You represent a chemical company that is being...Ch. 7.1 - What are the two types of hypotheses used in a...Ch. 7.1 - Describe the two types of errors possible in a...Ch. 7.1 - Prob. 3E Ch. 7.1 - Does failing to reject the null hypothesis mean...Ch. 7.1 - True or False? In Exercises 510, determine whether...

Knowledge Booster

$Statistics$

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.

The null and alternative hypotheses. To run: The simulation so that at least 1,000 hypothesis tests are run. To compare: The proportion of null hypothesis rejections for the 0.05 level and the 0.01 level. To perform: The hypotheses test for each level.

Solution Summary: The author explains the null and alternative hypotheses.

Concept explainers

Videos

To find: The null and alternative hypotheses. To run: The simulation so that at least 1,000 hypothesis tests are run. To compare: The proportion of null hypothesis rejections for the 0.05 level and the 0.01 level. To perform: The hypotheses test for each level.

Want to see the full answer?

Chapter 7 Solutions

To find: The null and alternative hypotheses.

To run: The simulation so that at least 1,000 hypothesis tests are run.

To compare: The proportion of null hypothesis rejections for the 0.05 level and the 0.01 level.

To perform: The hypotheses test for each level.