Over the course of five days, I gathered data on how many people visited Kern Café between noon and 1 pm.  Using this information, I calculated the average number of daily visitors, along with the standard deviation and a 95% confidence interval to better understand the typical visitor count. This analysis shows the trends in customer activity at Kern Café and demonstrates how statistical tools can infer population parameters from sample data.

Methods

The following dataset represents the number of people who entered Kern Café between noon and 1 pm over five consecutive days. The mean (x̄) and standard deviation (s) are computed as follows:

kern_data = [28, 24, 33, 37, 29]
mean = np.mean(kern_data)
std_dev = np.std(kern_data, ddof=1)

To estimate the average number of daily visitors to Kern Café with a 95% level of confidence, the margin of error (MOE) is calculated using the t-distribution:

C = 0.95
n = 5
df = 4
t_star = t.ppf(1 - (1 - C) / 2, df)
moe = t_star * std_dev / np.sqrt(n)

The 95% confidence interval is calculated:

x_bar=mean
x_bar-moe, x_bar + moe

Results

Using the collected data, the following values were computed:

Mean Results:  30.2

Standard Deviation Results: 4.969909455915671

T-Statistic Results: 2.7764451051977987

Margin of Error Results: 6.170957645742957

Confidence Interval Results: 24.029042354257044, 36.370957645742955

Interpretation

On average, about 30 people visit Kern Café each day, based on the data collected. However, since this is just an estimate from a small sample, the actual average could be different. With 95% confidence, we can say the true daily average likely falls somewhere between 24 and 36 visitors. This range reflects the variability in the data and the uncertainty that comes with using a limited sample size. The relatively wide range suggests that gathering more data could help narrow down and refine this estimate.

Conclusion

This analysis shows how statistical methods can be used to make sense of real-world data. Calculating a 95% confidence interval provided a useful range for estimating the average daily number of visitors to Kern Café. However, collecting data over a longer period or with a larger sample size could help make these estimates even more precise. With more time, I would have also done a more randomized sample. Regardless, with this information, Kern Café’s management could gain valuable insights into customer trends and better plan for busy periods, especially if similar studies are done for other times of the day.