Hard Work, a studio releases a new video game. The studio believes that the game will be liked by players; in particular, the studio claims that the mean player rating, μ, will be higher than 85. In a random sample of 39 players, the mean rating is 88.6. Assume the population standard deviation of the ratings is known to be 23.6. Is there enough evidence to support the claim that the mean player rating is higher than 85? Perform a hypothesis test, using the 0.10 level of significance. (a) State the null hypothesis Ho and the alternative hypothesis H₁. μ Ho: D H₁: 0 0<0 OSO 020 0=0 メロ X S ? (b) Perform a Z-test and find the p-value. Here is some information to help you with your Z-test. x-μ . The value of the test statistic is given by O √n • The p-value is the area under the curve to the right of the value of the test statistic. |x □口
Hard Work, a studio releases a new video game. The studio believes that the game will be liked by players; in particular, the studio claims that the mean player rating, μ, will be higher than 85. In a random sample of 39 players, the mean rating is 88.6. Assume the population standard deviation of the ratings is known to be 23.6. Is there enough evidence to support the claim that the mean player rating is higher than 85? Perform a hypothesis test, using the 0.10 level of significance. (a) State the null hypothesis Ho and the alternative hypothesis H₁. μ Ho: D H₁: 0 0<0 OSO 020 0=0 メロ X S ? (b) Perform a Z-test and find the p-value. Here is some information to help you with your Z-test. x-μ . The value of the test statistic is given by O √n • The p-value is the area under the curve to the right of the value of the test statistic. |x □口
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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I don't understand how it's done exactly how u get the p value
![### Testing a Hypothesis for a New Video Game Release
After a lot of hard work, a studio releases a new video game. The studio believes that the game will be liked by players; in particular, the studio claims that the mean player rating, μ, will be higher than 85. In a random sample of 39 players, the mean rating is 88.6. Assume the population standard deviation of the ratings is known to be 23.6.
**Objective:** Determine if there is enough evidence to support the claim that the mean player rating is higher than 85 by performing a hypothesis test using the 0.10 level of significance.
#### Steps:
1. **State the Hypotheses:**
- **Null Hypothesis (\(H_0\))**: The mean player rating is 85. \[ H_0: \mu = 85 \]
- **Alternative Hypothesis (\(H_1\))**: The mean player rating is greater than 85. \[ H_1: \mu > 85 \]
2. **Perform a Z-test and find the \(p\)-value.**
- **Test Statistic Calculation:**
The value of the test statistic (Z) is calculated using the formula:
\[
Z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}
\]
Where:
- \(\bar{x}\) is the sample mean (88.6)
- \(\mu\) is the population mean (85)
- \(\sigma\) is the population standard deviation (23.6)
- \(n\) is the sample size (39)
- **P-Value:**
The \(p\)-value represents the area under the curve to the right of the value of the test statistic in a Standard Normal Distribution.
3. **Explanation of Graph:**
The provided graph depicts a Standard Normal Distribution curve with a shaded area representing the \(p\)-value.
**Steps to Shade the Area Represented by the \(p\)-value:**
- **Step 1:** Select one-tailed or two-tailed test.
- Options: One-tailed or Two-tailed.
- **Step 2:** Enter the test statistic (round to 3 decimal places).
- **Step 3:** Shade the area represented](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffd1b6d45-a7eb-422c-8cfa-b963b51ff783%2F5000314a-434b-49cb-bf62-de1fe8ba9959%2Ffsa3ak5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Testing a Hypothesis for a New Video Game Release
After a lot of hard work, a studio releases a new video game. The studio believes that the game will be liked by players; in particular, the studio claims that the mean player rating, μ, will be higher than 85. In a random sample of 39 players, the mean rating is 88.6. Assume the population standard deviation of the ratings is known to be 23.6.
**Objective:** Determine if there is enough evidence to support the claim that the mean player rating is higher than 85 by performing a hypothesis test using the 0.10 level of significance.
#### Steps:
1. **State the Hypotheses:**
- **Null Hypothesis (\(H_0\))**: The mean player rating is 85. \[ H_0: \mu = 85 \]
- **Alternative Hypothesis (\(H_1\))**: The mean player rating is greater than 85. \[ H_1: \mu > 85 \]
2. **Perform a Z-test and find the \(p\)-value.**
- **Test Statistic Calculation:**
The value of the test statistic (Z) is calculated using the formula:
\[
Z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}
\]
Where:
- \(\bar{x}\) is the sample mean (88.6)
- \(\mu\) is the population mean (85)
- \(\sigma\) is the population standard deviation (23.6)
- \(n\) is the sample size (39)
- **P-Value:**
The \(p\)-value represents the area under the curve to the right of the value of the test statistic in a Standard Normal Distribution.
3. **Explanation of Graph:**
The provided graph depicts a Standard Normal Distribution curve with a shaded area representing the \(p\)-value.
**Steps to Shade the Area Represented by the \(p\)-value:**
- **Step 1:** Select one-tailed or two-tailed test.
- Options: One-tailed or Two-tailed.
- **Step 2:** Enter the test statistic (round to 3 decimal places).
- **Step 3:** Shade the area represented
![**Introduction to Hypothesis Tests for the Population Mean Using Standard Normal Distribution**
**Step 1:** Select one-tailed or two-tailed.
- One-tailed
- Two-tailed
**Step 2:** Enter the test statistic. (Round to 3 decimal places.)
- [Input Field]
**Step 3:** Shade the area represented by the p-value.
- [Shading Icon]
**Step 4:** Enter the p-value. (Round to 3 decimal places.)
- [Input Field]
**Diagram Explanation:**
The accompanying graph is a bell-shaped standard normal distribution curve. The x-axis ranges from -3 to 3, while the y-axis displays the probability density with values such as 0.1, 0.2, 0.3, and 0.4. The graph illustrates the symmetrical nature of the normal distribution, peaking at the center around the mean (0 on the x-axis).
**Step (c):** Based on your answer to part (b), choose what can be concluded, at the 0.10 level of significance, about the claim made by the studio.
- Since the p-value is less than (or equal to) the level of significance, the null hypothesis is rejected. So, there is enough evidence to support the claim that the mean player rating is higher than 85.
- Since the p-value is less than (or equal to) the level of significance, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the mean player rating is higher than 85.
- Since the p-value is greater than the level of significance, the null hypothesis is rejected. So, there is enough evidence to support the claim that the mean player rating is higher than 85.
- Since the p-value is greater than the level of significance, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the mean player rating is higher than 85.
**Buttons:**
- Explanation [ ]
- Check [ ]
© 2022 McGraw Hill LLC. All Rights Reserved.
Terms of Use | Privacy Center | Accessibility](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffd1b6d45-a7eb-422c-8cfa-b963b51ff783%2F5000314a-434b-49cb-bf62-de1fe8ba9959%2Fwrqsxbm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Introduction to Hypothesis Tests for the Population Mean Using Standard Normal Distribution**
**Step 1:** Select one-tailed or two-tailed.
- One-tailed
- Two-tailed
**Step 2:** Enter the test statistic. (Round to 3 decimal places.)
- [Input Field]
**Step 3:** Shade the area represented by the p-value.
- [Shading Icon]
**Step 4:** Enter the p-value. (Round to 3 decimal places.)
- [Input Field]
**Diagram Explanation:**
The accompanying graph is a bell-shaped standard normal distribution curve. The x-axis ranges from -3 to 3, while the y-axis displays the probability density with values such as 0.1, 0.2, 0.3, and 0.4. The graph illustrates the symmetrical nature of the normal distribution, peaking at the center around the mean (0 on the x-axis).
**Step (c):** Based on your answer to part (b), choose what can be concluded, at the 0.10 level of significance, about the claim made by the studio.
- Since the p-value is less than (or equal to) the level of significance, the null hypothesis is rejected. So, there is enough evidence to support the claim that the mean player rating is higher than 85.
- Since the p-value is less than (or equal to) the level of significance, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the mean player rating is higher than 85.
- Since the p-value is greater than the level of significance, the null hypothesis is rejected. So, there is enough evidence to support the claim that the mean player rating is higher than 85.
- Since the p-value is greater than the level of significance, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the mean player rating is higher than 85.
**Buttons:**
- Explanation [ ]
- Check [ ]
© 2022 McGraw Hill LLC. All Rights Reserved.
Terms of Use | Privacy Center | Accessibility
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