The company intends to evaluate the effectiveness of customer service training. The average time spent per customer before the training was 14 minutes. The service manager randomly selects some employees who recently completed the training and measures the time spent per customer. Can the training be considered effective, and has it had the desired impact on the average time? Use a significance level of 5%.
a) Formulate the hypotheses.
b) Choose an appropriate test method and calculate the test statistic.
c) Formulate the null hypothesis rejection rule.
d) Draw a correct conclusion based on the hypothesis test result.
e) Could the null hypothesis also be rejected with a confidence level of 99%? Justify your answer.
The data on the time spent per customer by the selected employees are as follows:
9, 10, 7, 9, 8, 6, 12, 10, 9, 8, 12, 11, 9, 10, 9, 7, 9, 8, 10, 9, 11, 14, 8, 7, 9, 10, 7, 6
Walking right now🚶♀️will give it a go when near computer and get back to you tanel.
sounds amazing, probably will be asleep by then, as it's almost 3am and i'm doing some last minute cramming 💜
will check first thing in the morning 🤗
How many employees are there? Seems like you'd need to know that to disprove the null hypothesis, which would be due to a disproportionately small sample size.
Okay so keeping in mind your sample size is 28, benchmark is 14, average time spent with customers is 9.07, std dev is 1.86, std error is 0.35 which leads to a t-stat of -13.99. The hypothesis could be any of following:
P-value
5% critical value (one-sided upper tail test)
1.HO: m <14 (benchmark)
2.HA: m>14 (benchmark)
3. Test using p-value:
T-stat: remember coefficient-benchmark/ std error which is 9.07-14/0.35 =-13.99
P-value: 1.00
4.Decision rule at 5% significance level: reject null if p<0.05:
a)p-value >0.05 fail to reject
5.Conclusion
There is insufficient evidence at the 5% significance level to conclude that the average time spent per customer is greater than 14 minutes.
P-value
5% critical value (one-sided lower tail test)
1.HO: m >14 (benchmark)
2.HA: m<14 (benchmark)
3. Test using p-value:
T-stat: remember coefficient-benchmark/ std error which is 9.07-14/0.35 =-13.99
P-value: 0.00
4.Decision rule at 5% significance level: reject null if p<0.05:
a)p-value <0.05 reject
5.Conclusion
There is sufficient evidence at the 5% significance level to conclude that the average time spent per customer is less than 14 minutes.
P-value benchmark, any difference or not the same
5% critical value (Two-sided test)
1.HO: m =14 (benchmark)
2.HA: m≠ 14 benchmark)
3. Test using p-value:
T-stat: remember coefficient-benchmark/ std error which is 9.07-14/0.35 =-13.99
P-value: 0.00
4.Decision rule at 5% significance level: reject null if p<0.05:
a)p-value <0.05 reject
5.Conclusion
There is sufficient evidence the average time spent per customer is not at benchmark at 5% significance level.
Confidence Interval benchmark (two-sided test)
1. HO: μ = b (14)
2.HA: μ ≠ b (14)
3. Test using 95% confidence interval:
(8.38, 9.76) lower bound and upper bound.
4. Decision rule: reject if 14 outside of the 95% CI
a) 14 is outside the CI - reject
5. Conclusion
We are 95% confident that the average time spent per customer is not performing at the original benchmark of 14 being the time taken before the training was implemented. Instead, the average time post training is now between 8.38 and 9.76.
Confidence Interval benchmark (two-sided test)
1. HO: μ = b (14)
2.HA: μ ≠ b (14)
3. Test using 99% confidence interval:
(8.16, 9.98) lower bound and upper bound
4. Decision rule: reject if 14 outside of the 99% CI
a) 14 is outside the CI - reject
5. Conclusion
We are 99% confident that the average time spent per customer is not performing at the original benchmark of 14 being the time taken before the training was implemented. Instead, the average time post training is now between 8.16 and 9.98.
Hope this helps tanel :)
thank you so much, glanced over this in the morning and it helped a ton 💜
just finished the final and have a rather good feeling about it
Happy to hear it went well tanel :)
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