### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# MGt 218 : Chapter 9 : Hypothesis tests about the Mean and proportion MGT 218

Marshall

GPA 3.72

### View Full Document

## 10

## 0

## Popular in Introductory Statistics

## Popular in Business

This 5 page Class Notes was uploaded by Winn on Thursday March 31, 2016. The Class Notes belongs to MGT 218 at Marshall University taught by in Spring 2016. Since its upload, it has received 10 views. For similar materials see Introductory Statistics in Business at Marshall University.

## Reviews for MGt 218 : Chapter 9 : Hypothesis tests about the Mean and proportion

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 03/31/16

Chapter 9 : Hypothesis T ests about the Mean and Proportion. Book : Introductory Statistics – Prem S.Mann Explaining Important More Important This lesson explains how to conduct a hypothesis test of a mean, when the following conditions are met: The sampling method is simple random sampling. The sampling distribution is normal or nearly normal. Generally, the sampling distribution will be approximately normally distributed if any of the following conditions apply. The population distribution is normal. The population distribution is symmetric, unimodal, without outliers, and the sample size is 15 or less. The population distribution is moderately skewed, unimodal, without outliers, and the sample size is between 16 and 40. The sample size is greater than 40, without outliers. This approach consists of four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. State the Hypotheses Every hypothesis test requires the analyst to state a null hypothesis and an alternative hypothesis. The hypotheses are stated in such a way that they are mutually exclusive. That is, if one is true, the other must be false; and vice versa. The table below shows three sets of hypotheses. Each makes a statement about how the population mean μ is related to a specified value M. (In the table, the symbol ≠ means " not equal to ".) Null Alternative Number of Set hypothesis hypothesis tails 1 μ = M μ ≠ M 2 2 μ > M μ < M 1 3 μ < M μ > M 1 The first set of hypotheses (Set 1) is an example of a two-tailed test, since an extreme value on either side of the sampling distribution would cause a researcher to reject the null hypothesis. The other two sets of hypotheses (Sets 2 and 3) are one-tailed tests, since an extreme value on only one side of the sampling distribution would cause a researcher to reject the null hypothesis Hypothesis Testing For a Population Mean The Idea of Hypothesis Testing Suppose we want to show that only children have an average higher cholesterol level than the national average. It is known that the mean cholesterol level for all Americans is 190. Construct the relevant hypothesis test: H : m = 190 0 H 1 m > 190 We test 100 only children and find that x = 198 and suppose we know the population standard deviation s = 15. Do we have evidence to suggest that only children have an average higher cholesterol level than the national average? We have z is called the test statistic. Since z is so high, the probability that Ho is true is so small that we decide to reject H0and accept H . 1herefore, we can conclude that only children have a higher average cholesterol level than the national average. Rejection Regions Suppose that a = .05. We can draw the appropriate picture and find the z score for -.025 and .025. We call the outside regions the rejection regions. We call the blue areas the rejection region since if the value of z falls in these regions, we can say that the null hypothesis is very unlikely so we can reject the null hypothesis Example 50 smokers were questioned about the number of hours they sleep each day. We want to test the hypothesis that the smokers need less sleep than the general public which needs an average of 7.7 hours of sleep. We follow the steps below. A. Compute a rejection region for a significance level of .05. B. If the sample mean is 7.5 and the population standard deviation is 0.5, what can you conclude? Solution First, we write write down the null and alternative hypotheses H 0 m = 7.7 H 1 m < 7.7 This is a left tailed test. The z-score that corresponds to .05 is -1.645. The critical region is the area that lies to the left of -1.645. If the z- value is less than -1.645 there we will reject the null hypothesis and accept the alternative hypothesis. If it is greater than -1.645, we will fail to reject the null hypothesis and say that the test was not statistically significant. We have Since -2.83 is to the left of -1.645, it is in the critical region. Hence we reject the null hypothesis and accept the alternative hypothesis. We can conclude that smokers need less sleep.

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

#### "I bought an awesome study guide, which helped me get an A in my Math 34B class this quarter!"

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

#### "Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.