Susu Le
Susi Le
Ashley Abalos
P. 4
Final Project
II. Data Report
To achieve random samples, we put the digits 125 on pieces of paper and put them all into a bowl. The digits correspond to the days starting from April 16th to May 10th. For example, April 16th corresponds to 1, and April 17th corresponds to 2. We pulled out 7 random pieces of paper from the bowl and went to Tpumps and Kung Fu Tea on these particular days. Ashley went to Tpumps while Susu and Susi went to Kung Fu Tea. We bought 5 boba cups from both places on the assigned days around 45pm. We collected our data by counting the number of boba pearls in each drink as we drank them. We made sure to order the same size (regular) from both places.
Our populations are Tpumps drinks and Kung Fu Tea drinks. We are confident that our samples match our populations because we selected random days to go collect our data. Because our sample sizes of 35 boba drinks from each place are > 30, our samples are large.
We avoided undercoverage bias for various days by selecting the days to buy boba randomly and not buying all of the drinks in our samples in just one day. We did not avoid undercoverage bias for time of day because we did not collect data throughout the day. Different times of day may cause workers to put different amounts of boba in each drink. For instance, workers may put more boba pearls per drink at the end of the day because the shop is closing soon so they want to get rid of all the leftover boba pearls. Another example of undercoverage bias is how we did not take into consideration the time of year, such as the seasons. Workers may put less boba pearls in each drink during the summer because more people drink boba since the weather is warmer; therefore, workers must conserve boba pearls to satisfy the high demand for boba.
We think that our results generalize to all boba drink sizes from Tpumps and Kung Fu Tea, not just their regular size drinks. We believe Kung Fu Tea workers generally put more boba pearls in each of their drinks than Tpumps workers do.
III. Exploring the Data
Summary statistics:

As seen in the summary stats and the dotplots above, the center of the Tpumps distribution (36.29 boba pearls) is much lower than the center of the Kung Fu Tea distribution (91.17 boba pearls). The spread for the Tpumps distribution (6.43 boba pearls) is less than the spread for the Kung Fu Tea distribution (12.51 boba pearls). The dotplots above show that the distribution of each sample is symmetrical.
The boxplot for Tpumps shows that the Tpumps distribution has one high outlier of 53 boba pearls.
IV. Analyzing the Data
Name: 2mean ttest
Hypotheses:
HO: μK = μT (μK = the true mean boba count in Kung Fu drinks)
HA: μK ≠ μT (μT = the true mean boba count in Tpumps drinks)
Conditions:
2 independent samples √
Randomized samples √
n=35>30 for both samples, so by CLT, difference between x̅’s ≈ normal
Math:
X̅K = 91.17 sK = 12.51 nK = 35
X̅T = 36.29 sT = 6.43 nT = 35
t = ((91.1736.29)0)/√((12.51^2/35)+(6.43^2/35)) = 23.09
p = 0
df = 50.81
α = 0.05
Conclusion: With a pvalue of 0<α, I reject HO. We found statistically significant evidence that the true mean boba count in Kung Fu drinks is different than the true mean boba count in Tpumps drinks.
Name: 2mean tinterval
Math:
(X̅K  X̅T) ± t*SD = (91.1736.29) ± 1.675(2.853) ⇾ (50.11, 59.66)
Conclusion: I am 95% confident that the true difference between the means of boba count is between 50.11 and 59.66 boba pearls.
Grand Conclusion:
Although we did avoid the undercoverage bias for various days by not buying all of the drinks in the same day, we did not avoid the undercoverage bias for time of day. This bias could have caused an underestimate of the parameter for Tpumps’s drinks because most of Tpumps customers are high school students while Kung Fu customers vary, so the 45pm time range may have been a busy time for Tpumps; therefore, they put less boba in their drinks to conserve boba. However, since the pvalue is so small and the confidence interval is so far off from 0, we did find statistically significant evidence that there is a difference between the boba count of Kung Fu drinks and of Tpumps drinks. The difference is so large that any sampling variability or biases that we did not avoid could not account for all of it. Therefore, we can conclude from our data that Kung Fu puts more boba pearls into their drinks than Tpumps.
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