A local bank claims that the waiting time for its customers to be served is the lowest in the area. A competitor bank checks the waiting times at both banks. The sample statistics are listed below. Test the local bank's claim. Use the information given below. Use a significance level of .05 and assume the variances are equal. Sample statistics for a local bank and a competitor's bank Local Bank Competitor Bank Sample size nj = = 46 n2 = 50 Average waiting time in minutes for each sample X = 2.3 mins. X2 = 2.6 Sample Standard Deviation of each Sample S1 = 1.1 mins 1.0 mins. S2 %3D 1. Are the samples dependent or independent? 2. State your Null/Alternative hypotheses 3. What is the test-statistic? 4. What is the p-value? 5. What are the critical values? 6. Does the test-statistic lie in the rejection region? 7. Interpret the Result? nge for a different yalue of alpha? Explain?
A local bank claims that the waiting time for its customers to be served is the lowest in the area. A competitor bank checks the waiting times at both banks. The sample statistics are listed below. Test the local bank's claim. Use the information given below. Use a significance level of .05 and assume the variances are equal. Sample statistics for a local bank and a competitor's bank Local Bank Competitor Bank Sample size nj = = 46 n2 = 50 Average waiting time in minutes for each sample X = 2.3 mins. X2 = 2.6 Sample Standard Deviation of each Sample S1 = 1.1 mins 1.0 mins. S2 %3D 1. Are the samples dependent or independent? 2. State your Null/Alternative hypotheses 3. What is the test-statistic? 4. What is the p-value? 5. What are the critical values? 6. Does the test-statistic lie in the rejection region? 7. Interpret the Result? nge for a different yalue of alpha? Explain?
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
Transcribed Image Text:### Analyzing Bank Waiting Times
A local bank claims that its customer waiting time is the lowest in the area. To verify this claim, a competitor bank recorded the waiting times at both banks. The data collected is analyzed using a significance level of 0.05, assuming equal variances.
#### Sample Statistics for a Local Bank and a Competitor's Bank
| Statistic | Local Bank (Group 1) | Competitor Bank (Group 2) |
|----------------------------------------|----------------------|---------------------------|
| **Sample size** | \( n_1 = 46 \) | \( n_2 = 50 \) |
| **Average waiting time (minutes)** | \( \bar{X}_1 = 2.3 \) mins | \( \bar{X}_2 = 2.6 \) mins |
| **Sample Standard Deviation (minutes)**| \( s_1 = 1.1 \) | \( s_2 = 1.0 \) |
#### Analysis Questions
1. **Are the samples dependent or independent?**
2. **State your Null/Alternative Hypotheses:**
- Null: There is no difference in waiting times between the two banks.
- Alternative: The local bank has shorter waiting times than the competitor.
3. **What is the test statistic?**
4. **What is the p-value?**
5. **What are the critical values?**
6. **Does the test statistic lie in the rejection region?**
7. **Interpret the Result:**
8. **Does the result change for a different value of alpha? Explain.**
This exercise helps in understanding hypothesis testing and statistical analysis using real-world scenarios.
Expert Solution
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Step 1
1.
Denote μ1, μ2 as the true average waiting time for all customers of local bank and competitor bank, respectively.
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