Answered: Complete the parts below to perform a…

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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Transcribed Image Text:### Understanding the Standard Normal Distribution #### Steps for Hypothesis Testing 1. **Select One-tailed or Two-tailed Test** - Options: - One-tailed - Two-tailed 2. **Enter the Critical Value(s)** - Guidance: Round to three decimal places. 3. **Enter the Test Statistic** - Guidance: Round to three decimal places. #### Graph Description - **Title:** Standard Normal Distribution - **Axes:** - **X-axis**: Represents the z-scores, ranging from -3 to 3. - **Y-axis**: Represents the probability density, ranging from 0 to 0.4. - **Curve:** A bell-shaped curve indicating the standard normal distribution, peaking at the center (z = 0) and tapering off symmetrically towards the extremes. #### Application in Statistical Analysis **Contextual Task:** - (d) Based on your previous answer, determine the conclusion at a 0.10 level of significance regarding the proportion of dentists recommending the brand. This setup is typically used in hypothesis testing to evaluate statistical significance and make informed decisions based on data analysis.

$According to a report done last year by the dental industry, 81% of dentists would recommend Starry Whites toothpaste. After some recent negative publicity, the sales team at Starry Whites suspects the proportion of dentists who now recommend the brand is lower. The team chooses 150 dentists at random and asks them whether they'd recommend the brand. Of those, 118 say they'd recommend it. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.10 level of significance, to conclude that the proportion, $ p $, of all dentists who now recommend this brand is less than 81%. (a) State the null hypothesis $ H_0 $ and the alternative hypothesis $ H_1 $ that you would use for the test. - $ H_0: $ - $ H_1: $ [There are symbols for selecting the null and alternative hypothesis, including $ = $, $ \neq $, $ < $, $ > $, with $ p $ and $ \hat{p} $.] (b) For your hypothesis test, you will use a Z-test. Find the values of $ np $ and $ n(1-p) $ to confirm that a Z-test can be used. (One standard is that $ np \geq 10 $ and $ n(1-p) \geq 10 $ under the assumption that the null hypothesis is true.) Here $ n $ is the sample size and $ p $ is the population proportion you are testing.$

Transcribed Image Text:According to a report done last year by the dental industry, 81% of dentists would recommend Starry Whites toothpaste. After some recent negative publicity, the sales team at Starry Whites suspects the proportion of dentists who now recommend the brand is lower. The team chooses 150 dentists at random and asks them whether they'd recommend the brand. Of those, 118 say they'd recommend it. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.10 level of significance, to conclude that the proportion, $ p $, of all dentists who now recommend this brand is less than 81%. (a) State the null hypothesis $ H_0 $ and the alternative hypothesis $ H_1 $ that you would use for the test. - $ H_0: $ - $ H_1: $ [There are symbols for selecting the null and alternative hypothesis, including $ = $, $ \neq $, $ < $, $ > $, with $ p $ and $ \hat{p} $.] (b) For your hypothesis test, you will use a Z-test. Find the values of $ np $ and $ n(1-p) $ to confirm that a Z-test can be used. (One standard is that $ np \geq 10 $ and $ n(1-p) \geq 10 $ under the assumption that the null hypothesis is true.) Here $ n $ is the sample size and $ p $ is the population proportion you are testing.

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