Chapter 6.7, Problem 4E

The article “Time Series Analysis for Construction Productivity Experiments” (T. Abdelhamid and J. Everett. Journal of Construction Engineering and Management. 1999:87–95) presents a study comparing the effectiveness of a video system that allows a crane operator to see the lifting point while operating the crane with the old system in which the operator relies on hand signals from a tagman. Three different lifts, A, B, and C, were studied. Lift A was of little difficulty, lift B was of moderate difficulty, and lift C was of high difficulty. Each lift was performed several times, both with the new video system and with the old tagman system. The time (in seconds) required to perform each lift was recorded. The following tables present the means, standard deviations, and sample sizes.

1. a. Can you conclude that the mean time to perform a lift of low difficulty is less when using the video system than when using the tagman system? Explain.
2. b. Can you conclude that the mean time to perform a lift of moderate difficulty is less when using the video system than when using the tagman system? Explain.
3. c. Can you conclude that the mean time to perform a lift of high difficulty is less when using the video system than when using the tagman system? Explain.

To determine

Check whether there is evidence to conclude that the mean time to perform a lift of low difficulty is less when using the video system than when using the tagman system.

Answer to Problem 4E

There is no evidence to conclude that the mean time to perform a lift of low difficulty is less when using the video system than when using the tagman system.

Explanation of Solution

Given info:

Three different lifts, A, B, and C, were studied in the given experiment. Lift A was of little difficulty, lift B was of moderate difficulty, and lift C was of high difficulty. The summary statistics for three lifts are given below:

Low difficulty:

Tagman: $\overline{X}=47.79$, $s_X=2.19$ and $n_X=14$

Video: $\overline{Y}=47.15$, $s_Y=2.65$ and $n_Y=40$

Moderate difficulty:

Tagman: $\overline{X}=69.33$, $s_X=6.26$ and $n_X=12$

Video: $\overline{Y}=58.50$, $s_Y=5.59$ and $n_Y=24$

High difficulty:

Tagman: $\overline{X}=109.71$, $s_X=17.02$ and $n_X=17$

Video: $\overline{Y}=84.52$, $s_Y=13.51$ and $n_Y=29$

Calculation:

State the test hypotheses.

Null hypothesis:

$H_0:{\mu }_X-{\mu }_Y\le 0$

Alternative hypothesis:

$H_1:{\mu }_X-{\mu }_Y>0$

Tests statistic and P-value:

Software Procedure:

Step-by-step procedure to obtain the test statistic using the MINITAB software:

• Choose Stat > Basic Statistics > 2-Sample t.
• Choose Summarized data.
• In first, enter Sample size as 14, Mean as 47.79, Standard deviation as 2.19.
• In second, enter Sample size as 40, Mean as 47.15, Standard deviation as 2.65.
• Choose Options.
• In Confidence level, enter 95.
• In Alternative, select greater than.
• Click OK in all the dialogue boxes.

Output using the MINITAB software is given below:

From the MINITAB output, the test statistic is 0.89 and the P-value is 0.191.

Conclusion:

The P-value is 0.191 and the significance level is 0.05.

Here, the P-value is greater than the significance level.

That is, $0.191\left(=P\text{-value}\right)>0.05\left(=\alpha \right)$.

Therefore, the null hypothesis is not rejected.

Thus, there is no evidence to conclude that the mean time to perform a lift of low difficulty is less when using the video system than when using the tagman system.

To determine

Check whether there is evidence to conclude that the mean time to perform a lift of moderate difficulty is less when using the video system than when using the tagman system.

Answer to Problem 4E

There is evidence to conclude that the mean time to perform a lift of moderate difficulty is less when using the video system than when using the tagman system.

Explanation of Solution

Calculation:

State the test hypotheses.

Null hypothesis:

$H_0:{\mu }_X-{\mu }_Y\le 0$

Alternative hypothesis:

$H_1:{\mu }_X-{\mu }_Y>0$

Tests statistic and P-value:

Software Procedure:

Step-by-step procedure to obtain the test statistic using the MINITAB software:

• Choose Stat > Basic Statistics > 2-Sample t.
• Choose Summarized data.
• In first, enter Sample size as 12, Mean as 69.33, Standard deviation as 6.26.
• In second, enter Sample size as 24, Mean as 58.50, Standard deviation as 5.59.
• Choose Options.
• In Confidence level, enter 95.
• In Alternative, select greater than.
• Click OK in all the dialogue boxes.

Output using the MINITAB software is given below:

From the MINITAB output, the test statistic is 5.07 and the P-value is 0.000.

Conclusion:

The P-value is 0.000 and the significance level is 0.05.

Here, the P-value is less than the significance level.

That is, $0.000\left(=P\text{-value}\right)<0.05\left(=\alpha \right)$.

Therefore, the null hypothesis is rejected.

Thus, there is evidence to conclude that the mean time to perform a lift of moderate difficulty is less when using the video system than when using the tagman system.

To determine

Check whether there is evidence to conclude that the mean time to perform a lift of high difficulty is less when using the video system than when using the tagman system.

Answer to Problem 4E

There is evidence to conclude that the mean time to perform a lift of high difficulty is less when using the video system than when using the tagman system.

Explanation of Solution

Calculation:

State the test hypotheses.

Null hypothesis:

$H_0:{\mu }_X-{\mu }_Y\le 0$

Alternative hypothesis:

$H_1:{\mu }_X-{\mu }_Y>0$

Tests statistic and P-value:

Software Procedure:

Step-by-step procedure to obtain the test statistic using the MINITAB software:

• Choose Stat > Basic Statistics > 2-Sample t.
• Choose Summarized data.
• In first, enter Sample size as 17, Mean as 109.71, Standard deviation as 17.02.
• In second, enter Sample size as 29, Mean as 84.52, Standard deviation as 13.51.
• Choose Options.
• In Confidence level, enter 95.
• In Alternative, select greater than.
• Click OK in all the dialogue boxes.

Output using the MINITAB software is given below:

From the MINITAB output, the test statistic is 5.21 and the P-value is 0.000.

Conclusion:

The P-value is 0.000 and the significance level is 0.05.

Here, the P-value is less than the significance level.

That is, $0.000\left(=P\text{-value}\right)<0.05\left(=\alpha \right)$.

Therefore, the null hypothesis is rejected.

Thus, there is evidence to conclude that the mean time to perform a lift of high difficulty is less when using the video system than when using the tagman system.