Independent random samples, each containing 60 observations, were selected from two populations. The **Statistical Test for Difference in Proportions**We have samples from two populations where samples from populations 1 and 2 produced 20 and 10 successes, respectively. We are tasked with testing the hypothesis:- Null Hypothesis ($H_0$): $ (p_1 - p_2) = 0 $- Alternative Hypothesis ($H_a$): $ (p_1 - p_2) > 0 $We will use a significance level of $ \alpha = 0.01 $.**Questions:**(a) The test statistic is [Input Box](b) The P-value is [Input Box]This section is designed for educational purposes, intended to facilitate the understanding of hypothesis testing for differences in proportions. Adjust the values in the input boxes based on your computations.

To determine the test statistics and p-value.

Answered: samples from populations 1 and 2…

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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A researcher is interested in exploring the relationship between calcium intake and weight loss. Two different groups, each with 2626 dieters, are chosen for the study. Group A is required to follow a specific diet and exercise regimen, and also take a 500-mg supplement of calcium each day. Group B is required to follow the same diet and exercise regimen, but with no supplemental calcium. After six months on the program, the members of Group A had lost a mean of 10.4 pounds with a standard deviation of 2.6 pounds. The members of Group B had lost a mean of 11.7pounds with a standard deviation of 2.8 pounds during the same time period. Assume that the population variances are not the same. Construct a 99% confidence interval to estimate the true difference between the mean amounts of weight lost by dieters who supplement with calcium and those who do not. Let Population 1 be the amount of weight lost by Group A, who took a 500-mg supplement of calcium each day, and let Population 2 be…
Identify whether the studies described here are based on (1) single samples, (2) paired samples, or (3) independent samples. Cardiovascular disease risk factors are compared in husbands and wives. A nutritional exam is applied to a random sample of individuals. Results are compared to the results of the whole nation. An investigator compares vaccination histories in 30 autistic schoolchildren to a simple random sample of non-autistic children from the same school district.
IS IT REASONABLE TO ASSUME THIS SAMPLE CAME FROM A NORMAL POPULATION?
For each scenario listed below, determine whether the scenario represents an Independent Samples or Dependent Samples (Matched Pairs) situation by placing the appropriate letter in the box provided. a. Comparing pre-test scores before training to post-test scores: OIndependent Samples OMatched Pairs b. Comparing the number of speeding tickets received by men to the number received by women: OIndependent Samples Matched Pairs c. Comparing pain levels of a group receiving a placebo to a group receiving a medicine: Independent Samples OMatched Pairs d. Comparing pain levels before and after treatment with magnetic therapy: Independent Samples OMatched Pairs
When an audit must be conducted that involves a tedious examination of a large inventory, the audit may be very costly and time consuming if each item in the inventory must be examined. In such situations, the auditor frequently obtains a random sample of items from the complete inventory and uses the results of an audit of the sampled items to check the validity of the company's financial statement. A large company’s financial statement claims an inventory that averages $600 per item. The following data are the auditor’s assessment of a random sample of 75 items from the company’s inventory. The values resulting from the audit are rounded to the nearest dollar. Estimate the mean value of an item in the inventory using a 95% confidence interval. Is there substantial evidence (a 5 .01) that the mean value of an item in the inventory is less than $600? What is the target population for the above inferences? Would normal distribution–based procedures be appropriate for answering the…
2. Reporting on cheats What proportion of students are willing to report cheating by other students? A student project put this question to an SRS of 172 undergraduates at a large university: "You witness two students cheating on a quiz. Do you go to the professor?" Only 11% answered "Yes." The dotplot shows the proportion who would go to the professor in each of 1000 random samples of size 172 from a population where 11% would go to the professor. 17 0.1 0.15 0.2 0.25 Simulated sample proportion who would say "Yes" 0 0.05 Distribution of simulated proportion # samples 1000 mean 0.11 SD 0.024 (a) Use the results of the simulation to approximate the margin of error for Gallup's estimate of the proportion of U.S. adults who were satisfied with the way things were going in the United States at the time of the poll. (b) Interpret the margin of error.
If two large random samples are drawn from two populations, each having a mean of $100, the relevant sampling distribution of their difference has a mean of a. 200 b. The Sum of the 2 Sample Means C. 0 D. The difference between the two sample means.

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samples from populations 1 and 2 produced 20 and 10 successes, respectively. Test Ho: (P₁-P₂) = 0 against Ha : (P₁ − P2) > 0. Use a = 0.01 (a) The test statistic is (b) The P-value is