why are we using the number of events=19 for the sample proportion part of the equation, instead of the actual sample proportion=0.19?
why are we using the number of events=19 for the sample proportion part of the equation, instead of the actual sample proportion=0.19?
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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why are we using the number of
![Suppose that in a random selection of 100 colored candies, 19% of them are blue. The candy company claims that the percentage of blue candies is equal to 31%. Use a 0.05 significance level to test that claim.
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**Alternative Hypothesis: \( H_1: p \neq 0.31 \)**
The test statistic is a value used in making a decision about the null hypothesis. It is found by converting the sample statistic (such as \( \hat{p}, \bar{x}, \) or \( s \)) to a score (such as \( z, t, \) or \( \chi^2 \)) with the assumption that the null hypothesis is true. While the test statistic can be found using technology or the equation below, where \( \hat{p} \) is the sample proportion, \( p \) is the population proportion, \( q = 1 - p, \) and \( n \) is the sample size, for this problem use technology.
\[
z = \frac{\hat{p} - p}{\sqrt{\frac{pq}{n}}}
\]
Identify the number of events, the number of trials, the claimed population proportion, and the significance level to be used in technology.
The number of events is 19, the number of trials is 100, the claimed population proportion is 0.31, and the significance level is 0.05.
Use technology to identify the test statistic for this hypothesis test, rounding to two decimal places.
The test statistic for this hypothesis test is \(-2.59\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F60e5fca3-b9c2-47c4-9eba-5478d8641133%2Fcc27f533-6eb2-432c-b577-ba13d727379e%2Fia44bp7_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose that in a random selection of 100 colored candies, 19% of them are blue. The candy company claims that the percentage of blue candies is equal to 31%. Use a 0.05 significance level to test that claim.
---
**Alternative Hypothesis: \( H_1: p \neq 0.31 \)**
The test statistic is a value used in making a decision about the null hypothesis. It is found by converting the sample statistic (such as \( \hat{p}, \bar{x}, \) or \( s \)) to a score (such as \( z, t, \) or \( \chi^2 \)) with the assumption that the null hypothesis is true. While the test statistic can be found using technology or the equation below, where \( \hat{p} \) is the sample proportion, \( p \) is the population proportion, \( q = 1 - p, \) and \( n \) is the sample size, for this problem use technology.
\[
z = \frac{\hat{p} - p}{\sqrt{\frac{pq}{n}}}
\]
Identify the number of events, the number of trials, the claimed population proportion, and the significance level to be used in technology.
The number of events is 19, the number of trials is 100, the claimed population proportion is 0.31, and the significance level is 0.05.
Use technology to identify the test statistic for this hypothesis test, rounding to two decimal places.
The test statistic for this hypothesis test is \(-2.59\).
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