Show All Your Work If The Problem Requires It Part 11

Show All Of Your Work If The Problem Requires Itpart 11if You Use A

Show ALL of your work if the problem requires it. PART 1 #1 If you use a 95% confidence level in a two-tail hypothesis test, what will you decide about your Null Hypothesis if the computed value of the test statistic is Z = 2.57? Why? #2. You are the manager of a restaurant for a fast-food franchise. Last month, the mean waiting time at the drive- through window for branches in your geographical region, as measured from the time a customer places an order until the time the customer receives the order, was 3.7 minutes. You select a random sample of 64 orders. The sample mean waiting time is 3.57 minutes, with a sample standard deviation of 0.8 minute. a) At a 95% confidence level, is there evidence that the population mean waiting time is different from 3.7 minutes? b) Because the sample size is 64, do you need to be concerned about the shape of the population distribution when conducting the t- test in (a)? Explain. PART 2 For this week you will need to read sections 9.1 and 9.2 in your textbook and go over the lecture notes. Watch the following videos as a supplement 9.1 Hypothesis Testing with a known standard deviation 9.2 Hypothesis testing with an unknown standard deviation ( t-test) The problems below are from Chapter 9. #1 is from 9.1 and 9.2. You will use the Critical Value Approach to Hypothesis Testing ( both the Z test and t test). #1. CHAPTER 9: HYPOTHESIS TESTING an example problem A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages are labeled as 8 ounces, the company wants the packages to contain a mean of 8.17 ounces so that virtually none of the packages contain less than 8 ounces. A sample of 50 packages is selected periodically, and the packaging process is stopped if there is evidence that the mean amount packaged is different from 8.17 ounces. Suppose that in a particular sample of 50 packages, the mean amount dispensed is 8.159 ounces, with a population standard deviation of 0.051 ounce. Is there evidence that the population mean amount is different from 8.17 ounces? (Use a 95% confidence level). a. State the variables and their assigned value according to the problem ( X (Sample Mean), μ (population mean), n (sample size), σ (Standard deviation)) b. According to the information, state the Null and the Alternative Hypothesis. c. State the level of significance, α according to the problem d. What is the appropriate test and why? e. Determine the critical Values according to the α value in part c f. Compute the value of the test statistic (Hint since we are in chapter 9, you will be using the Z test for the mean with a known standard deviation) g. Make a statistical decision, determine whether the assumptions are valid, and the managerial conclusion in the context of the theory, claim, or assertion being tested. If the test statistic falls into the nonrejection region, you do not reject the null hypothesis. If the test statistic falls into the rejection region, you reject the null hypothesis. #2. CHAPTER 9: HYPOTHESIS TESTING One of the major measures of the quality of service provided by any organization is the speed with which it responds to customer complaints. A large family-held department store selling furniture and flooring, including carpet, had undergone a major expansion in the past several years. Last year there were 50 complaints concerning carpet installation. Suppose that the manager analyzes the data of 50 complaints and computes the following: Average time to respond to a customer complaint = 23 days Standard deviation = 3 days a) The installation supervisor claims that the population mean number of days between the receipt of a complaint and the resolution of the complaint is 20 days. At the 95% confidence level, is there evidence that the claim is not true (i.e., that the mean number of days is different from 20)? i. State the variables and their assigned value according to the problem ( X (Sample Mean), μ (population mean), n (sample size), σ (Standard deviation)) ii. According to the information, state the Null and the Alternative Hypothesis. iii. State the level of significance, α according to the problem iv. What is the appropriate test and why? v. Determine the critical Values according to the α value in part c vi. Compute the value of the test statistic (Hint since we are in chapter 9, you will be using the t test for the mean with a known standard deviation) vii. Make a statistical decision, determine whether the assumptions are valid, and the managerial conclusion in the context of the theory, claim, or assertion being tested. If the test statistic falls into the nonrejection region, you do not reject the null hypothesis. If the test statistic falls into the rejection region, you reject the null hypothesis. b) What assumption about the population distribution is needed in order to conduct the t-test in (a)?

Paper For Above instruction

Introduction

Hypothesis testing is a fundamental aspect of statistical analysis that allows researchers and decision-makers to make informed conclusions about population parameters based on sample data. It involves formulating hypotheses, selecting an appropriate test, and interpreting the results to determine whether there is enough evidence to support a specific claim or to refute it. This paper illustrates the application of hypothesis testing through real-world examples, emphasizing both z-tests and t-tests, and discusses the importance of choosing the correct method based on the data's characteristics.

Part 1: Hypothesis Testing in Practice

The first scenario involves testing a claim about a population mean waiting time at a fast-food drive-through. Suppose the null hypothesis states that the mean waiting time is equal to 3.7 minutes, and the alternative hypothesis suggests it differs from this value. Given a sample size of 64, a sample mean of 3.57 minutes, and a standard deviation of 0.8 minutes, we can perform a z-test because the sample size is sufficiently large. The critical z-value at a 95% confidence level for a two-tailed test is approximately ±1.96.

Calculating the z-statistic involves using the formula:

Z = (X̄ - μ) / (σ / √n) = (3.57 - 3.7) / (0.8 / √64) ≈ -1.75

Since the absolute value of -1.75 is less than 1.96, we fail to reject the null hypothesis, indicating there is no statistically significant evidence that the mean waiting time differs from 3.7 minutes at the 95% confidence level.

Part 2: Hypothesis Testing Examples

The second set of examples involves testing claims about packaging weights and customer service response times. In the chocolate packaging scenario, the sample mean of 8.159 ounces is compared to a hypothesized mean of 8.17 ounces. With a known standard deviation of 0.051 ounces and a sample size of 50, we use a z-test to determine if the mean differs significantly from 8.17 ounces. Calculating the test statistic:

Z = (8.159 - 8.17) / (0.051 / √50) ≈ -1.66

Similarly, for the customer service response time, the sample mean is 23 days with a standard deviation of 3 days, and the hypothesized mean is 20 days. Here, because the standard deviation is known and the sample size is 50, a z-test could be used. However, since the question specifies a t-test, assuming the population standard deviation is estimated from the sample, the t-test is appropriate. The test statistic:

t = (23 - 20) / (3 / √50) ≈ 8.366

This high t-value suggests rejecting the null hypothesis that the mean response time is 20 days, indicating a statistically significant difference.

Part 3: The Importance of Statistical Literacy

Statistical literacy refers to the ability to understand, interpret, and critically evaluate statistical information presented in various formats. It is an essential skill in today’s data-driven world, enabling individuals to make informed decisions, recognize misleading information, and contribute thoughtfully to discussions that involve quantitative data.

Being statistically literate means understanding fundamental concepts such as measures of central tendency, variability, hypothesis testing, confidence intervals, and the proper interpretation of statistical results. For example, a person with statistical literacy can evaluate claims made in media reports or advertisements, identify flawed methodologies, and assess the validity of conclusions based on data analysis.

In the context of decision-making, statistical literacy empowers managers, policymakers, and consumers to make better choices. For instance, interpreting clinical trial results or election polling requires a foundational understanding of statistics. Without this literacy, there’s a risk of succumbing to misinformation or misinterpreting data, which can lead to poor decisions or misconceptions.

Furthermore, increasing statistical literacy enhances critical thinking skills, fosters skepticism of unsupported claims, and promotes a culture of evidence-based reasoning. As data becomes more prevalent, the ability to analyze and interpret such information is crucial for personal, professional, and societal advancement.

In conclusion, being statistically literate is vital in an era where data influences almost every aspect of life. It enables individuals to approach information analytically, enabling better understanding and smarter decisions, ultimately contributing to a more informed society.

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