In Exercises 33–40, use the given probability value to determine whether the sample results are significant.




Selfie Deaths Based on Priceonomics data describing 49 deaths while taking selfies, it was found that 37 of those deaths were males. Assuming that males and females are equally likely to have selfie deaths, there is a 0.000235 probability of getting 37 or more males. Is the result of 37 males significantly low, significantly high, or neither? Does the result suggest that male selfie deaths are more likely than female selfie deaths?

Verified step by step guidance

1. Step 1: Understand the problem. The question asks whether the observed result (37 male selfie deaths out of 49 total deaths) is statistically significant, given the probability of observing 37 or more males is 0.000235. This involves comparing the given probability to a significance threshold (commonly 0.05 or 0.01).
2. Step 2: Recall the concept of statistical significance. A result is considered statistically significant if the probability of observing it (or something more extreme) is less than the chosen significance level (e.g., 0.05). This means the result is unlikely to occur by random chance alone.
3. Step 3: Compare the given probability (0.000235) to the typical significance level (e.g., 0.05). If the probability is less than the significance level, the result is considered statistically significant. If it is greater, the result is not significant.
4. Step 4: Interpret the significance. If the result is statistically significant, it suggests that the observed number of male selfie deaths is not due to random chance and may indicate a real difference in the likelihood of selfie deaths between males and females.
5. Step 5: Address the second part of the question. If the result is statistically significant, it supports the idea that male selfie deaths are more likely than female selfie deaths. If not, the data does not provide strong evidence to support this claim.

Key Concepts

Significance Level

The significance level, often denoted as alpha (α), is a threshold used in hypothesis testing to determine whether to reject the null hypothesis. Commonly set at 0.05, it indicates the probability of making a Type I error, which is rejecting a true null hypothesis. In this context, if the probability of observing 37 or more males (0.000235) is less than the significance level, the result is considered statistically significant.

Null Hypothesis

The null hypothesis is a statement that assumes no effect or no difference in a given situation. In this case, it posits that males and females are equally likely to die while taking selfies. Testing the null hypothesis involves calculating the probability of observing the data under this assumption, which helps determine if the observed results are due to chance or indicate a real difference.

P-Value

The p-value is a statistical measure that helps determine the significance of the results from a hypothesis test. It represents the probability of obtaining results at least as extreme as the observed results, assuming the null hypothesis is true. A low p-value (typically less than 0.05) suggests that the observed data is unlikely under the null hypothesis, leading to the conclusion that the results are statistically significant.