An automobile dealer conducted a test to determine if the time in minutes needed to complete a minor engine tune-up depends on whether a computerized engine analyzer or an electronic analyzer is used. Because tune-up time varies among compact, intermediat full-sized cars, the three types of cars were used as blocks in the experiment. The data obtained follow. Analyzer Computerized Electronic Compact 48 41 Car Intermediate 57 44 Full-sized 63 47 Use a = 0.05 to test for any significant differences. State the null and alternative hypotheses. O Ho: Computerized Electronic Ha: "Computerized Electronic O Ho: "Compact Intermediate Full-sized Ha compact Intermediate Full-sized Ho compact * Intermediate Full-sized H: Compact Intermediate = Full-sized Ho: Computerized Electronic Compact Intermediate = Full-sized H: Not all the population means are equal. O Ho: Computerized Electronic Ha: Computerized Electronic Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. O Do not reject Ho. There is sufficient evidence to conclude that the mean tune-up times are not the same for both analyzers. O Reject Ho. There is not sufficient evidence to conclude that the mean tune-up times are not the same for both analyzers. O Do not reject Ho. There is not sufficient evidence to conclude that the mean tune-up times are not the same for both analyzers. O Reject Ho. There sufficient evidence to conclude that the mean tune-up times are not the same for both analyzers.
An automobile dealer conducted a test to determine if the time in minutes needed to complete a minor engine tune-up depends on whether a computerized engine analyzer or an electronic analyzer is used. Because tune-up time varies among compact, intermediat full-sized cars, the three types of cars were used as blocks in the experiment. The data obtained follow. Analyzer Computerized Electronic Compact 48 41 Car Intermediate 57 44 Full-sized 63 47 Use a = 0.05 to test for any significant differences. State the null and alternative hypotheses. O Ho: Computerized Electronic Ha: "Computerized Electronic O Ho: "Compact Intermediate Full-sized Ha compact Intermediate Full-sized Ho compact * Intermediate Full-sized H: Compact Intermediate = Full-sized Ho: Computerized Electronic Compact Intermediate = Full-sized H: Not all the population means are equal. O Ho: Computerized Electronic Ha: Computerized Electronic Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. O Do not reject Ho. There is sufficient evidence to conclude that the mean tune-up times are not the same for both analyzers. O Reject Ho. There is not sufficient evidence to conclude that the mean tune-up times are not the same for both analyzers. O Do not reject Ho. There is not sufficient evidence to conclude that the mean tune-up times are not the same for both analyzers. O Reject Ho. There sufficient evidence to conclude that the mean tune-up times are not the same for both analyzers.
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Author:Amos Gilat
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![### Determining the Effectiveness of Engine Analyzers on Tune-up Times
An automobile dealer conducted a test to determine if the time in minutes needed to complete a minor engine tune-up depends on whether a computerized engine analyzer or an electronic analyzer is used. To account for variability in tune-up times among different types of cars, the experiment included compact, intermediate, and full-sized cars. The observed data is summarized in the table below:
#### Tune-up Times (in minutes)
| Car Type | Computerized Analyzer | Electronic Analyzer |
|----------------|------------------------|----------------------|
| Compact | 48 | 41 |
| Intermediate | 57 | 44 |
| Full-sized | 63 | 47 |
The significance level for testing any significant differences is set to α = 0.05.
#### Hypotheses for Testing
State the null and alternative hypotheses:
1. **Hypothesis 1 (H₀):** The mean tune-up times are the same for both analyzers.
\[
H_0: \mu_{\text{Computerized}} = \mu_{\text{Electronic}}
\]
**Alternative Hypothesis 1 (H₃):** The mean tune-up times are different for each analyzer.
\[
H_3: \mu_{\text{Computerized}} \neq \mu_{\text{Electronic}}
\]
2. **Hypothesis 2 (H₀):** The mean tune-up times are the same for compact, intermediate, and full-sized cars.
\[
H_0: \mu_{\text{Compact}} = \mu_{\text{Intermediate}} = \mu_{\text{Full-sized}}
\]
**Alternative Hypothesis 2 (H₃):** The mean tune-up times are not the same for compact, intermediate, and full-sized cars.
\[
H_3: \mu_{\text{Compact}} \neq \mu_{\text{Intermediate}} \neq \mu_{\text{Full-sized}}
\]
3. **Hypothesis 3 (H₀):** All population means are equal.
\[
H_0: \mu_{\text{Computerized}} = \mu_{\text{Electronic}} = \mu_{\text{Compact}} = \mu_{\text{Intermediate}} = \mu_{\text{Full-sized}}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac470ff6-15fd-4fdc-a5f2-c97f7b5a1d30%2F90ff8e1b-6ac6-49c2-945b-2899dc575380%2Fonj16id_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Determining the Effectiveness of Engine Analyzers on Tune-up Times
An automobile dealer conducted a test to determine if the time in minutes needed to complete a minor engine tune-up depends on whether a computerized engine analyzer or an electronic analyzer is used. To account for variability in tune-up times among different types of cars, the experiment included compact, intermediate, and full-sized cars. The observed data is summarized in the table below:
#### Tune-up Times (in minutes)
| Car Type | Computerized Analyzer | Electronic Analyzer |
|----------------|------------------------|----------------------|
| Compact | 48 | 41 |
| Intermediate | 57 | 44 |
| Full-sized | 63 | 47 |
The significance level for testing any significant differences is set to α = 0.05.
#### Hypotheses for Testing
State the null and alternative hypotheses:
1. **Hypothesis 1 (H₀):** The mean tune-up times are the same for both analyzers.
\[
H_0: \mu_{\text{Computerized}} = \mu_{\text{Electronic}}
\]
**Alternative Hypothesis 1 (H₃):** The mean tune-up times are different for each analyzer.
\[
H_3: \mu_{\text{Computerized}} \neq \mu_{\text{Electronic}}
\]
2. **Hypothesis 2 (H₀):** The mean tune-up times are the same for compact, intermediate, and full-sized cars.
\[
H_0: \mu_{\text{Compact}} = \mu_{\text{Intermediate}} = \mu_{\text{Full-sized}}
\]
**Alternative Hypothesis 2 (H₃):** The mean tune-up times are not the same for compact, intermediate, and full-sized cars.
\[
H_3: \mu_{\text{Compact}} \neq \mu_{\text{Intermediate}} \neq \mu_{\text{Full-sized}}
\]
3. **Hypothesis 3 (H₀):** All population means are equal.
\[
H_0: \mu_{\text{Computerized}} = \mu_{\text{Electronic}} = \mu_{\text{Compact}} = \mu_{\text{Intermediate}} = \mu_{\text{Full-sized}}
\]
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