### Hypothesis Test for the Difference Between Two Population Proportions**Overview:**A state housing department is attempting to ascertain if housing prices in County B are lower than those in County A. The department conducted a random sampling of recently sold houses in both counties, focusing on houses sold for more than $250,000. Given that County A is significantly larger than County B, a larger sample was drawn from County A. The data collected is summarized below.**Data Summary:**| | County A | County B ||----------------------|--------------------|------------------|| **Successes** | 366 | 192 || **Observations** | 700 | 400 || **p-hat** | 0.523 | 0.48 |**Statistical Analysis:**- **Confidence Level:** 90%- **z-score:** -1.372- **p-value:** 0.085**Graphical Representation:**- A normal distribution curve is displayed with a shaded region corresponding to the z-score of -1.372. This shaded area indicates the region of rejection for the hypothesis test at a 90% confidence level.### Detailed Explanation:The hypothesis test aims to determine if the proportion of houses sold for more than $250,000 in County B is significantly lower than in County A. The sample data provides the following:1. **Sample Sizes and Proportions:** - County A: - Sample Size ($ n_1 $) = 700 - Sample Proportion ($ \hat{p}_1 $) = 0.523 - County B: - Sample Size ($ n_2 $) = 400 - Sample Proportion ($ \hat{p}_2 $) = 0.482. **Hypothesis Testing:** - Null Hypothesis ($ H_0 $): No difference in the proportions ($ p_1 = p_2 $) - Alternative Hypothesis ($ H_a $): Proportion is greater in County A than in County B ($ p_1 > p_2 $)3. **Analysis and Interpretation:** - Given the z-score of -1.372 and the p-value of 0.085 at a 90% confidence level, the p-value exceeds the common significance level

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Answered: A state housing department is trying to…

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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Researchers investigated the issue of race and equality of access to clinical trials. The table below shows the population distribution and the number of participants in the clinical trials involving lung cancer. Use a 0.01 significance level to test the claim that the distribution of clinical trial participants fits well with the population distribution. Race/Ethnicity White Non-Hispanic Hispanic Black Asian/Pacific Islander American Indian/Alaskan Native Distribution of Population 75.6% 9.1% 10.8% 3.8% 0.7% Number in Lung Cancer Clinical Trials 3855 60 316 54 12 Complete the table below based on Problem. Note that do not round off on the whole computation of this problem. But please type the answers on the table by rounding it off to 2 decimal places. Hence, the answers on the table are rounded off to 2 decimal places but the process of computing this based on your solutions does not involve any rounding off. If the answer is negative, do not forget the negative sign. If…
Part II. Complete the ANOVA table below using the study description. Answer the questions to determine if there is in fact a significant difference between the three groups. A psychologist would like to examine the effects of sugar consumption on the activity level of preschool children. Three samples of children are selected with n = 5 in each sample. One group gets no sugar, one group gets a small dose, and the third group gets a large dose. The psychologist records the activity level for each child. The data from this experiment are presented below. 1. Do these data indicate any significant differences among the three groups? Test with α = .05.
Jump to level 1 The manager of a coffee shop is trying to determine if drive-through customers buy fewer items than customers who come into the shop. The manager randomly samples both populations and calculates the proportion of customers in each that buy three or more items. The results of the data collected are shown below. What are the population parameters? Pick Drive-through Successes Observations Proportion Confidence level Z-score p-value In-shop 41 Successes 119 Observations 0.345 Proportion 90% -0.1429 0.444 27 76 0.355 What is the level of significance? Ex: 0.12 Null hypothesis: Ho : Pdrive-through |Pick ✓ Pin-shop Alternative hypothesis: Ha : Pdrive-through Pick Pin-shop Should Ho be rejected or does Ho fail to be rejected? Pick What conclusion can be drawn from the data? Pick evidence exists to support the claim that drive-through customers buy fewer items than in-shop customers.
Which of the following data collection methods produces the highest level of evidence? Cross-sectional survey Case-control study Cohort study Systematic review
A sales analyst wants to determine whether there is a difference in the mean monthly sales of a company's four sales regions. Several salespersons from each region are randomly selected and they provide their sales amount (in thousands of dollars) for the previous month. Using a 5% significance, can we conclude at least one region is different on average? Region Sales North North North North East East East East East South South South South West West West West West 21 36 33 28 28 35 31 35 39 12 22 7 27 23 30 27 31 39 What is the factor variable? [Select an answer What is the response variable? [Select an answer Test Statistic: P-Value: Decision Rule: Select an answer Did Something Significant Happen? Select an answer There Select an answer to conclude Select an answer
A standardized exam consists of three parts: math, writing, and critical reading. Sample data showing the math and writing scores for a sample of 12 students who took the exam follow. Student Math Writing 1 540 474 2 432 380 3 528 457 4 574 612 5 448 420 6 502 520 7 480 430 8 499 459 9 610 615 10 572 535 11 390 329 12 593 613 Use a 0.05 level of significance and test for a difference between the population mean for the math scores and the population mean for the writing scores. (Use math score − writing score.) 1. Calculate the test statistic. (Round your answer to three decimal places.) 2. Calculate the p-value. (Round your answer to four decimal places.) p-value =
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Part c please
A power analysis is a calculation used to estimate the smallest sample size needed for an experiment, given a required significance level, statistical power, and effect size. It helps to determine if a result from an experiment or survey is due to chance, or if it is genuine and significant. Think of an experiment or a survey that you have conducted or will conduct in your field of interest and use it to discuss the following questions: 1. Describe the importance of power analysis in an experiment. 2. How will you determine the appropriate significance level for a power analysis? 3. Explain, in your own words, how you will conduct a power analysis in your experiment or survey.
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An auditor for a local court system is tasked with comparing the rulings of two judges. The auditor needs to determine if Judge Hughes issues shorter sentences than Judge Wilson. The data below are the sentence lengths, in months, issued by each judge in their last twelve cases that dealt with operating a motor vehicle without a license. Test the claim that Judge Hughes issues shorter sentences than Judge Wilson for this particular type of case at the 0.05 level of significance. Let Judge Hughes' sentences be Population 1 and let Judge Wilson's sentences be Population 2. Assume that both populations are approximately normal and that the population variances are equal. Judge 24 12 12 30 Hughes 36 30 12 18 24 12 24 30 Judge 36 36 24 24 24 24 18 12 30 24 18 30 Wilson Copy Data Step 2 of 3: Compute the value of the test statistic. Round your answer to three decimal places.

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