According to past studies, 26% of gamers experience motion sickness from using virtual reality (VR) glasses. Because of changes to the way VR glasses are manufactured, a consumer advocate claims the proportion, p, of gamers who will experience motion sickness from using modern VR glasses is more than 26% He tests his caim by choosing 190 gamers at random and having each of them use a pair of newly-manufactured VR glasses. Of these gamers, 55 say that using the glasses makes them motion sick. 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 gamers who will experience motion sickness from using modern VR glasses is greater than 26%.
According to past studies, 26% of gamers experience motion sickness from using virtual reality (VR) glasses. Because of changes to the way VR glasses are manufactured, a consumer advocate claims the proportion, p, of gamers who will experience motion sickness from using modern VR glasses is more than 26% He tests his caim by choosing 190 gamers at random and having each of them use a pair of newly-manufactured VR glasses. Of these gamers, 55 say that using the glasses makes them motion sick. 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 gamers who will experience motion sickness from using modern VR glasses is greater than 26%.
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Transcribed Image Text:## Steps for Hypothesis Testing Using Standard Normal Distribution
### Step-by-Step Instructions
**Step 1:** Select one-tailed or two-tailed test.
- Options:
- One-tailed
- Two-tailed
**Step 2:** Enter the test statistic.
- Round to three decimal places.
**Step 3:** Shade the area represented by the p-value on the graph.
**Step 4:** Enter the p-value.
- Round to three decimal places.
### Graph Explanation
The graph displayed is a standard normal distribution curve, bell-shaped and symmetric about the mean. The x-axis is labeled with values typically ranging from -3 to 3, and the curve peaks at the center with decreasing tails on either side. The area under the curve represents probabilities, with critical regions shaded based on the test being performed.
### Decision Making (Hypothesis Testing)
**Part (d):** Based on the p-value calculated, determine the conclusion at the 0.10 level of significance regarding the proportion of gamers who experience motion sickness from using modern VR glasses.
Options:
- 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 conclude that more than 26% of all gamers will experience motion sickness from using modern VR glasses.
- 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 conclude that more than 26% of all gamers will experience motion sickness from using modern VR glasses.
- Since the p-value is greater than the level of significance, the null hypothesis is rejected. So, there is enough evidence to conclude that more than 26% of all gamers will experience motion sickness from using modern VR glasses.
- Since the p-value is greater than the level of significance, the null hypothesis is not rejected. So, there is not enough evidence to conclude that more than 26% of all gamers will experience motion sickness from using modern VR glasses.
### Controls
- Options included for checking answers and accessing explanations.
**Note:** This educational exercise guides users through hypothesis testing, focusing on interpreting p-values and making statistical conclusions.
All rights reserved © 2021 McGraw Hill LLC.
![### Hypothesis Testing for Motion Sickness in Gamers Using VR Glasses
According to past studies, 26% of gamers experience motion sickness from using virtual reality (VR) glasses. A consumer advocate claims the proportion, \( p \), of gamers who will experience motion sickness from using modern VR glasses is more than 26%. To test this claim, the advocate randomly selects 190 gamers and provides them with newly-manufactured VR glasses. Out of these gamers, 55 report feeling motion sickness.
The objective is to determine if there is enough evidence, at a 0.10 level of significance, to conclude that more than 26% of all gamers will experience motion sickness with modern VR glasses.
#### Steps to Perform a Hypothesis Test
**(a) State the Hypotheses:**
- **Null Hypothesis (\( H_0 \)):** \( p = 0.26 \)
- This hypothesis states that the proportion of gamers who experience motion sickness is 26%.
- **Alternative Hypothesis (\( H_1 \)):** \( p > 0.26 \)
- This hypothesis suggests that the proportion is greater than 26%.
**(b) Conditions for Using a Z-test:**
To use a z-test, check the values of \( np \) and \( n(1-p) \) to ensure they meet the requirements \( np \geq 10 \) and \( n(1-p) \geq 10 \).
- **Calculations:**
- \( np = 49.4 \)
- \( n(1-p) = 140.6 \)
Since both conditions are satisfied, a z-test is appropriate.
**(c) Perform a Z-test and Find the p-value:**
- **Test Statistic Formula:**
\[
\text{Test Statistic} = \frac{\hat{p} - p}{\sqrt{\frac{p(1-p)}{n}}}
\]
- **P-value:**
- The p-value represents the area under the normal distribution curve to the right of the calculated test statistic.
The z-test and p-value will help determine if there's sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.
#### Conclusion
Use the z-test results to evaluate the consumer advocate’s claim. If the p-value is less than the significance level (0.10), reject the null hypothesis in favor of the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53adddb0-ebb2-4e76-a872-01ab126d1a60%2F00129afb-a677-4846-a998-6a835668e6b4%2Fb6cukqs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing for Motion Sickness in Gamers Using VR Glasses
According to past studies, 26% of gamers experience motion sickness from using virtual reality (VR) glasses. A consumer advocate claims the proportion, \( p \), of gamers who will experience motion sickness from using modern VR glasses is more than 26%. To test this claim, the advocate randomly selects 190 gamers and provides them with newly-manufactured VR glasses. Out of these gamers, 55 report feeling motion sickness.
The objective is to determine if there is enough evidence, at a 0.10 level of significance, to conclude that more than 26% of all gamers will experience motion sickness with modern VR glasses.
#### Steps to Perform a Hypothesis Test
**(a) State the Hypotheses:**
- **Null Hypothesis (\( H_0 \)):** \( p = 0.26 \)
- This hypothesis states that the proportion of gamers who experience motion sickness is 26%.
- **Alternative Hypothesis (\( H_1 \)):** \( p > 0.26 \)
- This hypothesis suggests that the proportion is greater than 26%.
**(b) Conditions for Using a Z-test:**
To use a z-test, check the values of \( np \) and \( n(1-p) \) to ensure they meet the requirements \( np \geq 10 \) and \( n(1-p) \geq 10 \).
- **Calculations:**
- \( np = 49.4 \)
- \( n(1-p) = 140.6 \)
Since both conditions are satisfied, a z-test is appropriate.
**(c) Perform a Z-test and Find the p-value:**
- **Test Statistic Formula:**
\[
\text{Test Statistic} = \frac{\hat{p} - p}{\sqrt{\frac{p(1-p)}{n}}}
\]
- **P-value:**
- The p-value represents the area under the normal distribution curve to the right of the calculated test statistic.
The z-test and p-value will help determine if there's sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.
#### Conclusion
Use the z-test results to evaluate the consumer advocate’s claim. If the p-value is less than the significance level (0.10), reject the null hypothesis in favor of the
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