On Average, A Banana Will Last 7 Days From Purchase

On Average A Banana Will Last 7 Days From The Time It Is Purchase

On average, a banana will last 7 days from the time it is purchased in the store to the time it is too rotten to eat. A study was conducted to determine whether hanging bananas from the ceiling affects their shelf life. Data from an experiment with 16 bananas hung from the ceiling were collected: 7.7, 5.2, 4.5, 6.3, 7.9, 7.7, 8.2, 6.5, 4.2, 6, 5, 6.5, 7.2, 7.6, 4.6, 7.6. The population distribution is assumed to be normal.

The hypothesis test aims to assess if the mean spoilage time for bananas hung from the ceiling is less than 7 days. Relevant statistical tests include a t-test for a population mean, given the small sample size and unknown population variance.

Paper For Above instruction

In assessing whether the practice of hanging bananas from the ceiling extends or reduces their shelf life, a one-sample t-test provides an appropriate statistical framework. The null hypothesis (H₀) posits that there is no difference in the mean spoilage time; specifically, H₀: μ = 7 days. Conversely, the alternative hypothesis (H₁) suggests that hanging bananas decreases their spoilage time: H₁: μ

The sample data provided are: 7.7, 5.2, 4.5, 6.3, 7.9, 7.7, 8.2, 6.5, 4.2, 6, 5, 6.5, 7.2, 7.6, 4.6, 7.6. Firstly, the sample mean (x̄) is calculated to determine the central tendency:

Sample mean, x̄ = (Sum of data points) / 16 = (97.8) / 16 = 6.1125 days.

Next, the sample standard deviation (s) is computed to measure variability, which results in approximately 1.547 days. The test statistic (t) is calculated using the formula:

t = (x̄ - μ₀) / (s / √n) = (6.1125 - 7) / (1.547 / √16) = (-0.8875) / (1.547 / 4) = (-0.8875) / 0.38675 ≈ -2.297.

With 15 degrees of freedom (n-1), the associated p-value for this t-statistic (approximately -2.297) in a one-tailed test is approximately 0.0171. Since the p-value (0.0171) exceeds the significance level (α=0.01), we fail to reject the null hypothesis. This indicates there isn't sufficient statistical evidence to conclude that hanging bananas from the ceiling significantly reduces their spoilage time at the 1% significance level.

In conclusion, although the sample mean suggests a slight decrease from 7 days, the evidence isn’t strong enough at α=0.01 to confirm that hanging bananas decreases their spoilage duration. Future studies with larger samples or alternative methodologies may provide more definitive insights.

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