**Step 1: Test Set-up**Tony V. owns a house painting business in Seattle. He estimates that it takes his crew three-and-a-half days to paint the interior of a typical house. He has no estimate of the population standard deviation, σ. He is testing a new paint that is supposed to dry faster than the paint he has been using for over thirty years. He estimates that the average time to paint a house is 3.5 days, meaning the new paint is just as good as the old paint and costs the same.**Research Question:** Does the new paint allow him to complete a house painting job faster than the paint he has been using? He takes a random sample of 30 homes and paints them with the new paint. Here are the results:\[\begin{array}{cccccc}3.40 & 3.75 & 3.33 & 3.50 & 3.33 \\3.50 & 3.00 & 3.40 & 3.50 & 3.40 \\3.00 & 2.85 & 3.85 & 3.33 & 3.33 \\3.25 & 3.00 & 3.50 & 3.50 & 3.33 \\3.33 & 2.75 & 3.50 & 2.75 & 3.40 \\3.33 & 3.50 & 3.50 & 0.33 & 3.40 \\\end{array}\]The population mean, \( \mu \), is presumed to be 3.5 days and the population standard deviation, \( \sigma \), is unknown. Using Microsoft Excel, find the sample mean, \( \bar{X} \), and sample standard deviation, \( s \), and complete the appropriate significance test.**Questions:**1. **What statistical test should you use and why?** (There are three basic one-sample hypothesis tests: 1) z-test for the population mean, 2) z-test for the population proportion, and 3) t-test for the population mean.)2. **Based on the research question is this a left-tailed, two-tailed, or right-tailed test?**---**Step 2. Select the Level of Significance, \( \alpha \)**A 5 percent

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Step 1. Test Set-up Tony V. owns a house painting business in Seattle. He estimates that it takes his crew three-and-a-half days to paint the interior of a typical house. He has no estimate of the population standard deviation, o. He is testing a new paint that is supposed to dry faster than the paint he has been using for over thirty years. He estimates that the average time to paint a house is 3.5 days, the new paint is just as good as the old paint and costs the same. Research Question: Does the new paint allow him to complete a house painting job faster than the paint he has been using? He takes a random sample of 30 homes and paints them with the new paint. Here are the results: Number of Days to Paint House 3.40 3.75 3.33 3.50 3.33 3.50 3.00 3.40 3.50 3.40 3.00 2.85 3.85 3.33 3.33 3.50 3.33 3.33 2.75 3.50 2.75 3.40 3.33 3.50 3.50 0.33 3.40 3.25 3.00 3.50 The population mean, µ. is presumed to be 3.5 days and the population standard deviation, o, is unknown. Using Microsoft Excel, find the sample mean, X, and sample standard deviation, s, and complete the appropriate significance test. What O statistic should you use and why? (There are three basic one-sample hypothesis tests: 1) z-test for the population mean, 2) z-test for the population proportion, and 3) t-test for the population mean.) Based on the research question is this a left-tailed, two-tailed, or right-tailed test? Step 2. Select the Level of Significance, a A 5 percent significance level has been selected. What is the Critical Value or Values of the Test Statistic? Step 3. State the null hypothesis (Ho) and alternate hypothesis (H;) Ho: H:: Follow the examples shown in Clear-Sighted Statistics. You must use the appropriate Greek letters and mathematical symbols. = +s> 2 < n² | x² Step 4. Compose the decision rule using critical values not p-values. Follow the examples shown in Clear-Sighted Statistics. Step 5. Calculate the Value of the Test Statistic, p-value, Effect Size, Statistical Power and the Probability of a Type II Error

Step 1. Test Set-up Tony V. owns a house painting business in Seattle. He estimates that it takes his crew three-and-a-half days to paint the interior of a typical house. He has no estimate of the population standard deviation, o. He is testing a new paint that is supposed to dry faster than the paint he has been using for over thirty years. He estimates that the average time to paint a house is 3.5 days, the new paint is just as good as the old paint and costs the same. Research Question: Does the new paint allow him to complete a house painting job faster than the paint he has been using? He takes a random sample of 30 homes and paints them with the new paint. Here are the results: Number of Days to Paint House 3.40 3.75 3.33 3.50 3.33 3.50 3.00 3.40 3.50 3.40 3.00 2.85 3.85 3.33 3.33 3.50 3.33 3.33 2.75 3.50 2.75 3.40 3.33 3.50 3.50 0.33 3.40 3.25 3.00 3.50 The population mean, µ. is presumed to be 3.5 days and the population standard deviation, o, is unknown. Using Microsoft Excel, find the sample mean, X, and sample standard deviation, s, and complete the appropriate significance test. What O statistic should you use and why? (There are three basic one-sample hypothesis tests: 1) z-test for the population mean, 2) z-test for the population proportion, and 3) t-test for the population mean.) Based on the research question is this a left-tailed, two-tailed, or right-tailed test? Step 2. Select the Level of Significance, a A 5 percent significance level has been selected. What is the Critical Value or Values of the Test Statistic? Step 3. State the null hypothesis (Ho) and alternate hypothesis (H;) Ho: H:: Follow the examples shown in Clear-Sighted Statistics. You must use the appropriate Greek letters and mathematical symbols. = +s> 2 < n² | x² Step 4. Compose the decision rule using critical values not p-values. Follow the examples shown in Clear-Sighted Statistics. Step 5. Calculate the Value of the Test Statistic, p-value, Effect Size, Statistical Power and the Probability of a Type II Error

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 22PFA

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