A paint manufacturer wishes to compare the drying times of two different types of paint. Independent random samples of 11 cans of type A and 9 cans of type B were selected and applied to similar surfaces. The drying times (in hours) were recorded. The summary statistics are given in the image below. Use a 0.01 significance level to test the claim that the mean drying time for paint type A is longer than the mean drying time for paint type B. Find each: a) Set up (including Null and Alternative Hypothesis) b) Test Statistic c) P-value d) Conclusion (reject or accept H0).
A paint manufacturer wishes to compare the drying times of two different types of paint. Independent random samples of 11 cans of type A and 9 cans of type B were selected and applied to similar surfaces. The drying times (in hours) were recorded. The summary statistics are given in the image below. Use a 0.01 significance level to test the claim that the mean drying time for paint type A is longer than the mean drying time for paint type B. Find each: a) Set up (including Null and Alternative Hypothesis) b) Test Statistic c) P-value d) Conclusion (reject or accept H0).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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A paint manufacturer wishes to compare the drying times of two different types of paint. Independent random samples of 11 cans of type A and 9 cans of type B were selected and applied to similar surfaces. The drying times (in hours) were recorded. The summary statistics are given in the image below. Use a 0.01 significance level to test the claim that the
a) Set up (including Null and Alternative Hypothesis)
b) Test Statistic
c) P-value
d) Conclusion (reject or accept H0).

Transcribed Image Text:### Comparative Analysis of Two Types
This table represents a comparative analysis between two distinct types, labeled Type A and Type B. The comparison includes the mean (\(\bar{x}\)), standard deviation (\(s\)), and sample size (\(n\)) for each type.
#### Type A:
- **Mean (\(\bar{x}_1\))**: 76.9
- The average value for Type A is 76.9.
- **Standard Deviation (\(s_1\))**: 4.5
- This indicates the variability or dispersion of the data points around the mean for Type A is 4.5.
- **Sample Size (\(n_1\))**: 11
- The number of observations or data points collected for Type A is 11.
#### Type B:
- **Mean (\(\bar{x}_2\))**: 66.3
- The average value for Type B is 66.3.
- **Standard Deviation (\(s_2\))**: 5.1
- This signifies the variability or dispersion of the data points around the mean for Type B is 5.1.
- **Sample Size (\(n_2\))**: 9
- The number of observations or data points collected for Type B is 9.
This analysis provides a summary of the central tendencies and variability within both groups, which serves as a fundamental basis for further statistical comparison, such as t-tests or variance analyses, to determine if the observed differences are statistically significant.
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