ch 23 paper airplanes

Question

By randomly selecting between three different paper airplane models with a dice, Anna let #'s 1-2 represent model A, #'s 3-4 represent model B, and #'s 5-6 represent model C. She rolled a dice 2 times, and let the corresponding numbers she got be selected to each model. She did this and as a result chose models A and C. Two other group members and her conducted 30 tries per model, meaning a total of 60 tries were performed. Each individual in the group threw 10 times for every model, and each of the distances were recorded in cm as shown below:

Data:

model A (L1): 733.02, 699.06, 500, 416.51, 748.26, 578.74, 680.01, 633.02, 476.2, 455.88, 685.09, 860.96, 796.52, 612.7, 852.07, 868.58, 553.34, 702.54, 734.29, 613.97, 572.39, 613.97, 572.39, 462.23, 468.58, 562.23, 846.94, 866,96, 566.04, 202.54

model C (L2): 160, 68, 160, 187, 198,180, 84, 117, 176, 122, 82, 172, 193, 214, 140, 155, 175, 179, 150, 262, 185, 311, 160, 152, 108, 168, 155, 146, 162, 193

1. A. Use the appropriate hypothesis testing method to determine mathematically

which plane is the better model. Show your work and calculations below.

B. Interpret your conclusion in context. (Which airplane model is better because it

flies the farthest)?

C. Explain how your confidence interval supports or disputes your conclusion.

Answer 1

A. Hypothesis Test

To determine which airplane model is superior, a two-sample t-test was conducted to compare the mean flight distances of Models A and C.

Hypotheses:

H₀: μA = μC

Hₐ: μA > μC

where μA and μC represent the true mean flight distances of Models A and C, respectively.

Summary Statistics:

Model A:

n = 30

Mean = 639.54 cm

Standard Deviation = 170.50 cm

Model C:

n = 30

Mean = 165.40 cm

Standard Deviation = 50.61 cm

Test Statistic:

t = (639.54 − 165.40) / √[(170.50²/30) + (50.61²/30)]

t ≈ 14.60

The corresponding p-value is less than 0.0001.

Since the p-value is much smaller than α = 0.05, the null hypothesis is rejected.

B. Interpretation in Context

There is sufficient statistical evidence to conclude that Model A flies farther on average than Model C. The mean flight distance for Model A was approximately 639.54 cm, while the mean flight distance for Model C was approximately 165.40 cm. Therefore, Model A is the better airplane model because it consistently achieved greater flight distances.

C. Confidence Interval

A 95% confidence interval for the difference in population means (μA − μC) is:

474.14 ± 64.94

which gives:

(409.20 cm, 539.08 cm)

This means we are 95% confident that Model A flies between 409.20 cm and 539.08 cm farther, on average, than Model C.

The confidence interval supports the conclusion of the hypothesis test because the entire interval is positive and does not include 0. Since 0 is not a plausible value for the true difference in average flight distance, the interval provides strong evidence that Model A outperforms Model C. Both the confidence interval and the hypothesis test support the conclusion that Model A is the superior airplane design.