Question

The upcoming championship high school football game is a big deal in your little town. The problem is, it is being played in the next biggest town, which is two hours away! To get as many people as you can to attend the game, you decide to come up with a ride-sharing app, but you want to be sure it will be used before you put all the time in to creating it. You determine that if more than three students share a ride, on average, you will create the app.

You conduct simple random sampling of 20 students in a school with a population of 300 students to determine how many students are in each ride-share (carpool) on the way to school every day to get a good idea of who would use the app. The following data are collected:

6 5 5 5 3 2 3 6 2 2

5 4 3 3 4 2 5 3 4 5

Construct a 95% confidence interval for the mean number of students who share a ride to school, and interpret the results.

Part A: State the parameter and check the conditions.

Part B: Construct the confidence interval. Be sure to show all your work, including the degrees of freedom, critical value, sample statistics, and an explanation of your process.

Part C: Interpret the meaning of the confidence interval.

Part D: Use your findings to explain whether you should develop the ride-share app for the football game.

Answer 1

Solution:

Part A

The population parameter for this confidence interval is given as the population mean number of students who share a ride to school. For this research study, population size is adequate, and we assume that the population follows an approximately normal distribution.

Part B

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Xbar = 3.85

S = 1.348488433

n = 20

df = n – 1 = 20 – 1 = 19

Confidence level = 95%

Critical t value = 2.0930

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 3.85 ± 2.0930*1.348488433/sqrt(20)

Confidence interval = 3.85 ± 2.0930*0.30153118

Confidence interval = 3.85 ± 0.6311

Lower limit = 3.85 - 0.6311 = 3.2189

Upper limit = 3.85 + 0.6311 = 4.4811

Confidence interval = (3.2189, 4.4811)

Part C

We are 95% confident that the population mean number of students who share a ride to school will lies between two values 3.2189 and 4.4811.

Part D

We should develop the ride share app for the football game because the lower limit of the above interval is greater than 3. There is sufficient evidence to conclude that the average mean number of students who share a ride to school is greater than 3.