A coin-operated drink machine was designed to discharge a mean of 9 fluid ounces of coffee per cup. In a test of the machine, the discharge amounts in 18 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard deviation were 8.94 fluid ounces and 0.12 fluid ounces, respectively. If we assume that the discharge amounts are approximately normally distributed, is there enough evidence, to conclude that the population mean discharge, μ, differs from 9 fluid ounces? Use the 0.10 level of significance. Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H. and the alternative hypothesis H₁. H H₁:0 (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the p-value. (Round to three or more decimal places.) (e) Can we conclude that the mean discharge differs from 9 fluid ounces? OYes O No μ X O ロ S 2 6 3 0=0 OSO X P OO
A coin-operated drink machine was designed to discharge a mean of 9 fluid ounces of coffee per cup. In a test of the machine, the discharge amounts in 18 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard deviation were 8.94 fluid ounces and 0.12 fluid ounces, respectively. If we assume that the discharge amounts are approximately normally distributed, is there enough evidence, to conclude that the population mean discharge, μ, differs from 9 fluid ounces? Use the 0.10 level of significance. Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H. and the alternative hypothesis H₁. H H₁:0 (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the p-value. (Round to three or more decimal places.) (e) Can we conclude that the mean discharge differs from 9 fluid ounces? OYes O No μ X O ロ S 2 6 3 0=0 OSO X P OO
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:**Title: Statistical Hypothesis Testing of a Coffee Machine's Discharge Volume**
**Introduction:**
A coin-operated drink machine is designed to dispense a mean of 9 fluid ounces of coffee per cup. To verify its performance, the discharge volumes of coffee in 18 randomly selected cups were recorded. The sample produced a mean discharge of 8.94 fluid ounces with a standard deviation of 0.12 fluid ounces.
**Objective:**
Assuming the discharge volumes follow a normal distribution, we aim to determine whether there is sufficient evidence to conclude that the actual mean discharge differs from 9 fluid ounces, applying a significance level of 0.10.
**Procedure:**
- **Step (a): Formulate Hypotheses**
- Null Hypothesis (\(H_0\)): The population mean discharge \(\mu\) is 9 fluid ounces.
- Alternative Hypothesis (\(H_1\)): The population mean discharge \(\mu\) is not 9 fluid ounces.
- **Step (b): Select the Test Statistic**
- Choose an appropriate test statistic based on sample data characteristics.
- **Step (c): Compute the Test Statistic**
- Calculate the test statistic and round to three or more decimal places.
- **Step (d): Determine the \(p\)-value**
- Compute the \(p\)-value for the test statistic, ensuring precision to at least three decimal places.
- **Step (e): Make a Conclusion**
- Decide whether to reject the null hypothesis based on the \(p\)-value and the significance level of 0.10.
**Symbols and Equations Reference:**
A panel provides symbols commonly used in statistical calculations such as mean (\(\bar{x}\)), sample standard deviation (\(s\)), population parameter notation (\(\mu\), \(\sigma\)), and inequalities.
**Conclusion:**
Can we conclude that the discharge volume of the machine differs from the expected 9 fluid ounces?
Choose:
- Yes
- No
This exercise involves using hypothesis testing to assess whether variations in the machine's performance are statistically significant.
Expert Solution
Step 1: Information given is
sample size(n)=18
Mean(
)=8.94
standard deviation(s)=0.12
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