A random sample of n = 1,000 observations from a binomial population contained 378 successes. You wish to show that p < 0.4. n = 1,000 and x = 378. You wish to show that p < 0.4. n USE SALT Calculate the appropriate test statistic. (Round your answer to two decimal places.) z = Calculate the p-value. (Round your answer to four decimal places.) p-value = Do the conclusions based on a fixed rejection region of z < -1.645 agree with those found using the p-value approach at a = 0.05? O Yes, both approaches produce the same conclusion. O No, the p-value approach rejects the null hypothesis when the fixed rejection region approach fails to reject the null hypothesis. O No, the fixed rejection region approach rejects the null hypothesis when the p-value approach fails to reject the null hypothesis. Should they? O Yes
A random sample of n = 1,000 observations from a binomial population contained 378 successes. You wish to show that p < 0.4. n = 1,000 and x = 378. You wish to show that p < 0.4. n USE SALT Calculate the appropriate test statistic. (Round your answer to two decimal places.) z = Calculate the p-value. (Round your answer to four decimal places.) p-value = Do the conclusions based on a fixed rejection region of z < -1.645 agree with those found using the p-value approach at a = 0.05? O Yes, both approaches produce the same conclusion. O No, the p-value approach rejects the null hypothesis when the fixed rejection region approach fails to reject the null hypothesis. O No, the fixed rejection region approach rejects the null hypothesis when the p-value approach fails to reject the null hypothesis. Should they? O Yes
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 random sample of \( n = 1,000 \) observations from a binomial population contained 378 successes. You wish to show that \( p < 0.4 \).
\[ n = 1,000 \text{ and } x = 378. \text{ You wish to show that } p < 0.4. \]
**Calculate the appropriate test statistic.** (Round your answer to two decimal places.)
\[ z = \underline{\hspace{2cm}} \]
**Calculate the \( p \)-value.** (Round your answer to four decimal places.)
\[ p\text{-value} = \underline{\hspace{3cm}} \]
**Do the conclusions based on a fixed rejection region of \( z < -1.645 \) agree with those found using the \( p \)-value approach at \( \alpha = 0.05 \)?**
- ○ Yes, both approaches produce the same conclusion.
- ○ No, the \( p \)-value approach rejects the null hypothesis when the fixed rejection region approach fails to reject the null hypothesis.
- ○ No, the fixed rejection region approach rejects the null hypothesis when the \( p \)-value approach fails to reject the null hypothesis.
**Should they?**
- ○ Yes
- ○ No
You may need to use the appropriate appendix table to answer this question.
---
**Explanation for Educational Purposes:**
This exercise is a hypothesis test to determine if the proportion \( p \) from a binomial distribution is less than 0.4. The sample size is 1,000, with 378 successes observed. To solve this, the test statistic \( z \) and the \( p \)-value must be calculated. Based on the \( z \)-score, the decision to reject or not reject the null hypothesis is made by comparing it to a fixed rejection region or by using the \( p \)-value method. This study aims to see if these two approaches give the same conclusion at the significance level \( \alpha = 0.05 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb1c4ecf6-4fc7-4dd3-8c6c-f2aac9b21c6d%2F45aca734-5ce5-49c8-ad55-f7c83c229f68%2Fp3dpfb8_processed.png&w=3840&q=75)
Transcribed Image Text:A random sample of \( n = 1,000 \) observations from a binomial population contained 378 successes. You wish to show that \( p < 0.4 \).
\[ n = 1,000 \text{ and } x = 378. \text{ You wish to show that } p < 0.4. \]
**Calculate the appropriate test statistic.** (Round your answer to two decimal places.)
\[ z = \underline{\hspace{2cm}} \]
**Calculate the \( p \)-value.** (Round your answer to four decimal places.)
\[ p\text{-value} = \underline{\hspace{3cm}} \]
**Do the conclusions based on a fixed rejection region of \( z < -1.645 \) agree with those found using the \( p \)-value approach at \( \alpha = 0.05 \)?**
- ○ Yes, both approaches produce the same conclusion.
- ○ No, the \( p \)-value approach rejects the null hypothesis when the fixed rejection region approach fails to reject the null hypothesis.
- ○ No, the fixed rejection region approach rejects the null hypothesis when the \( p \)-value approach fails to reject the null hypothesis.
**Should they?**
- ○ Yes
- ○ No
You may need to use the appropriate appendix table to answer this question.
---
**Explanation for Educational Purposes:**
This exercise is a hypothesis test to determine if the proportion \( p \) from a binomial distribution is less than 0.4. The sample size is 1,000, with 378 successes observed. To solve this, the test statistic \( z \) and the \( p \)-value must be calculated. Based on the \( z \)-score, the decision to reject or not reject the null hypothesis is made by comparing it to a fixed rejection region or by using the \( p \)-value method. This study aims to see if these two approaches give the same conclusion at the significance level \( \alpha = 0.05 \).
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