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Summer Road Trips: A Comparison of Younger & Older Drivers
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1. Introduction

Summer is the best time to travel for many people as the weather gets warmer and children are finishing up the school year. With summer right around the corner, my wife and I have started to plan out the trips that we want to take. Though one of the trips will require a flight, travel for all of the other trips will be by means of our trusty old car, most requiring an overnight stay in the city we are visiting. After planning the logistics of the trips and making the necessary reservations, I was excited at the thought of the upcoming time off and chance to relax and refuel. I then proceeded to speak with my mother and ask if she could watch my dog for a few of the trips. I was surprised, however, to hear that she would not be able to watch my dog because she would be out of town on road trips herself that she had planned with friends. A few days later, I mentioned some of the trips I had planned to some colleagues at the office and some indicated that they, too, had road trips planned this summer. After further discussion with additional colleagues, I observed that many younger people were actually not going to go on many road trips this summer, while many older people actually had quite a few road trips planned.
This led me to wonder if older drivers, in general, had a higher likelihood of having road trips planned this summer than did younger drivers. The goal of this study was to determine the proportions of each group who had trips planned and understand whether or not there was a significant difference in the mean number of trips planned between each group.

2. Data Collection

I conducted a poll in order to collect the data that I would need to analyze any difference between the two groups. First, I determined what the parameters of the elements of my study would be. The study was a comparison of the frequency of summer road trips by driving planned between older and younger drivers, so I established older drivers as those 55 years of age and older and younger drivers as those between the ages of 18 and 34. Then, I determined that a road trip would be defined as a trip in which an overnight stay was required, so as to not include short, day road trips in the data. Second, I decided that the variables I was interested in for each element was the age of the respondent, whether they had any road trips planned this summer in which they were driving to and required at least one overnight stay, and the number of those type of trips that they had planned this summer. I then decided that I would set my sample size for each group at 50. I did this so that I would still acquire at least 30 respondents from each group who indicated they did have driving road trips planned this summer. With a sample size of at least 30 for each group, I would be able to test the frequency between both groups for any significant difference. After writing up the survey questions, I conducted the poll at a local mall collecting cross-sectional data between the dates of 4/19/14 and 4/20/14 among random shoppers until both sample sizes were satisfied. The original data collected and the poll questions are reported in the Appendix of this paper.

3. Statistical Analysis

With my recent observations of family and coworkers regarding their upcoming planned road trips, I thought that the data would reveal that older drivers were more likely to have such trips planned this summer than younger drivers. Data classification from the 100 respondents of the study are shown below in Table 1 and reveal a different story however.

Table 1. Contingency table of people who plan on taking at least one road trip driving this summer which will require at least one overnight stay by age group | Yes | No | Total | 18-34 | 41 | 9 | n₁=50 | 55+ | 33 | 17 | n₂=50 | Total | 74 | 26 | 100 |

To show various sample probabilities from the data collected, we use Table 1 to construct the probability table in Table 2 below.

Table 2. Probability table of people who plan on taking at least one road trip driving this summer which will require at least one overnight stay by age group | Yes | No | Total | 18-34 | 41.00% | 9.00% | 50.00% | 55+ | 33.00% | 17.00% | 50.00% | Total | 74.00% | 26.00% | 100.00% |

Contrary to my expectations coming into the study, Figure 1 below reveals that the proportion of younger drivers who had at least one road trip planned this summer that would require them driving to their destination and having at least one overnight stay was actually higher than that of older drivers in the study.

Figure 1. Proportion chart of people who plan on taking at least one road trip driving this summer which will require at least one overnight stay by age group

From Figure 1, we can compute the 95% confidence interval estimate between the two samples. That means we have an alpha of 0.05(5%) which is split into two equal tails. Looking up .025(2.5%) in the z-table provides us with a z-score of 1.96. Using the confidence interval estimation formula of (p1-hat minus p2-hat) ± 1.96 * sqrt (p1-hat * 1 – p1-hat / n₁) + (p2-hat * 1 – p2-hat / n₂), we find that the lower bound confidence interval is -0.0009 and the upper bound confidence interval is 0.3209 with a 95% confidence. Now that it appeared that younger drivers were actually more likely to have such road trips planned than older drivers, I wanted to test whether that difference was significant. To do this, I conducted a hypothesis test using a two-tailed z-test where the null hypothesis was π₀ - π₁ = 0 and the alternative hypothesis was π₀ - π₁ ≠ 0 with a 95% confidence.

Table 3. z-Test: Proportions of Two Populations | | | | | 18-34 | 55+ | Yes | 41 | 33 | Total | 50 | 50 | p1-hat | 0.8200 | | p2-hat | 0.6600 | | p-bar | 0.7400 | | q-bar | 0.2600 | | z | 1.8238 | |

The decision rule for the hypothesis test with a 95% confidence was that if │z*│ ≤ 1.96, then we would conclude the null hypothesis that there was no significant difference between the two proportions, otherwise we conclude the alternative. The Table 3 above shows that the z-score provided by the z-test for proportions of two populations is 1.8238, thus we conclude the null hypothesis since 1.8238 ≤ 1.96. Even though there was a difference in the proportion between the two groups, we must conclude the null hypothesis that the data do not provide sufficient evidence to indicate a significant difference between the two groups.
Next, I wanted to look at any difference in the number of trips planned this summer between younger and older drivers that required driving to the destination and at least one overnight stay. After running descriptive statistics between the two groups, shown below in Table 4, I was surprised to see that, contrary to the proportions for both groups, the mean number of trips for older drivers was actually more than a full point higher than the mean number of trips for younger drivers.

Table 4. Descriptive statistics of people who plan on taking at least one road trip driving this summer which will require at least one overnight stay by age group | 18-34 | 55+ | | Mean | 3.1707 | 4.2727 | | Standard Error | 0.3274 | 0.4486 | | Median | 3 | 4 | | Mode | 2 | 4 | | Standard Deviation | 2.0964 | 2.5772 | | Sample Variance | 4.3951 | 6.6420 | | Range | 10 | 11 | | Minimum | 1 | 1 | | Maximum | 11 | 12 | | Count | 41 | 33 | | Confidence Level (95.0%) | 0.6617 | 0.9138 |

Using Table 4 above, we see that the point estimate of the mean number of trips planned for younger drivers is 3.1707 and 4.2727 for older drivers. The confidence interval is between 2.509 and 3.8324 for younger drivers and between 3.3589 and 5.1865 for older drivers at the 95% confidence level.
To determine if the difference between the means of trips planned between younger and older drivers was significant, I conducted a two-tailed z-test where the null hypothesis was π₀ - π₁ = 0 and the alternative hypothesis was π₀ - π₁ ≠ 0 at the 95% confidence level, as shown below in Table 5. The decision rule for the hypothesis test with a 95% confidence was that if │z*│ ≤ 1.96, then we would conclude the null hypothesis that there was no significant difference between the two means, otherwise we conclude the alternative. With a z-score of│1.9841│>1.96, we reject the null hypothesis and the p-value is 0.0472. The conclusion is reject the null hypothesis and that there is a significant difference in the mean number of trips planned between younger and older drivers. Table 5. z-Test: Two Sample for Means | | | | | 18-34 | 55+ | Mean | 3.1707 | 4.2727 | Known Variance | 4.3951 | 6.6420 | Observations | 41 | 33 | Hypothesized Mean Difference | 0 | | z | -1.9841 | | P(Z<=z) two-tail | 0.0472 | |

4. Conclusion

The data analysis both confirmed and dismissed some of the expectations I had prior to the study. I had expected older drivers to have a higher likelihood of having at least one road trip planned this summer which required driving to the destination and at least one overnight stay, when compared to younger drivers. However, the study showed that the proportion of younger drivers who had planned trips this summer was actually higher than older drivers. Though the proportion was indeed higher, it was not significantly different after conducting a hypothesis test. The second aspect of the study did, nevertheless, confirm my expectation that older drivers had a higher likelihood of having more trips planned than younger drivers. With a mean of 4.2727 trips planned this summer, the difference between older drivers and younger drivers, with a mean of 3.1707, was indeed significantly different. Though the study did uncover some interesting insights that both confirmed and dismissed some of my expectations, a more robust sample size for both groups would help in reducing error and having a more concrete conclusion.

Appendix
Data Set:

Age Group | Road Trip Planned | # of Trips | | | Age Group | Road Trip Planned | # of Trips | 55+ | Yes | 5 | | | 18-34 | No | - | 55+ | Yes | 4 | | | 18-34 | No | - | 55+ | No | - | | | 18-34 | Yes | 2 | 55+ | Yes | 3 | | | 18-34 | Yes | 1 | 55+ | Yes | 7 | | | 18-34 | Yes | 2 | 55+ | Yes | 1 | | | 18-34 | Yes | 2 | 55+ | Yes | 4 | | | 18-34 | No | - | 55+ | No | - | | | 18-34 | Yes | 4 | 55+ | No | - | | | 18-34 | Yes | 2 | 55+ | Yes | 3 | | | 18-34 | Yes | 2 | 55+ | Yes | 2 | | | 18-34 | No | - | 55+ | Yes | 1 | | | 18-34 | Yes | 1 | 55+ | No | - | | | 18-34 | Yes | 3 | 55+ | Yes | 7 | | | 18-34 | Yes | 4 | 55+ | Yes | 2 | | | 18-34 | Yes | 4 | 55+ | Yes | 5 | | | 18-34 | Yes | 2 | 55+ | Yes | 4 | | | 18-34 | Yes | 4 | 55+ | Yes | 5 | | | 18-34 | Yes | 5 | 55+ | Yes | 11 | | | 18-34 | Yes | 2 | 55+ | Yes | 4 | | | 18-34 | Yes | 5 | 55+ | No | - | | | 18-34 | No | - | 55+ | No | - | | | 18-34 | No | - | 55+ | Yes | 4 | | | 18-34 | Yes | 8 | 55+ | Yes | 6 | | | 18-34 | Yes | 7 | 55+ | No | - | | | 18-34 | Yes | 2 | 55+ | Yes | 6 | | | 18-34 | Yes | 1 | 55+ | Yes | 12 | | | 18-34 | Yes | 1 | 55+ | No | - | | | 18-34 | No | - | 55+ | Yes | 1 | | | 18-34 | No | - | 55+ | No | - | | | 18-34 | Yes | 3 | 55+ | Yes | 7 | | | 18-34 | Yes | 6 | 55+ | No | - | | | 18-34 | Yes | 3 | 55+ | Yes | 3 | | | 18-34 | Yes | 5 | 55+ | No | - | | | 18-34 | Yes | 4 | 55+ | No | - | | | 18-34 | Yes | 2 | 55+ | Yes | 4 | | | 18-34 | Yes | 5 | 55+ | Yes | 3 | | | 18-34 | Yes | 2 | 55+ | No | - | | | 18-34 | Yes | 3 | 55+ | Yes | 5 | | | 18-34 | Yes | 4 | 55+ | No | - | | | 18-34 | Yes | 3 | 55+ | Yes | 1 | | | 18-34 | Yes | 1 | 55+ | Yes | 3 | | | 18-34 | Yes | 3 | 55+ | Yes | 6 | | | 18-34 | Yes | 1 | 55+ | Yes | 3 | | | 18-34 | Yes | 2 | 55+ | No | - | | | 18-34 | No | - | 55+ | No | - | | | 18-34 | Yes | 11 | 55+ | No | - | | | 18-34 | Yes | 1 | 55+ | Yes | 1 | | | 18-34 | Yes | 3 | 55+ | Yes | 4 | | | 18-34 | Yes | 2 | 55+ | Yes | 4 | | | 18-34 | Yes | 2 |
Poll Questions:

Q1. What is your age?

Q2. Do you plan on taking at least one road trip driving this summer which will require at least one overnight stay?

Q2. How many trips, requiring at least one overnight stay, do you plan on taking this summer?