Question

The local township has set a standard for its local fire department that it will respond to an emergency call within 8 minutes on 90% of all occurrences. Do the data from the past year suggest that the local fire department fails to meet this standard?

H₀:p=0.9
Hₐ:p<0.9

After conducting the test, the P -value is 0.044.

Based on sigma =0.05 , which of these is the correct conclusion for this hypothesis test?

a. We would reject the null hypothesis. This means that on the basis of the evidence, you can conclude that the proportion of responses within 8 minutes is greater than 90%.
b. We would reject the null hypothesis. This means that on the basis of the evidence, you can conclude that the proportion of responses within 8 minutes is less than 90%.
c. Do not reject the null hypothesis. This means that there is not enough evidence for you to conclude that the proportion of responses within 8 minutes is less than 90%.
d. Do not reject the null hypothesis. This means that there is enough evidence for you to conclude that the proportion of responses within 8 minutes is equal to 90%.

Answer 1

Since the P-value of 0.044 is less than the significance level of 0.05, we reject the null hypothesis, which indicates that the fire department likely fails to meet the 90% standard.

Step-by-step explanation:

The question at hand involves determining whether the local fire department meets the standard of responding to emergency calls within 8 minutes 90% of the time. The null hypothesis states that the proportion of responses within 8 minutes is 90% (H₀: p = 0.9), while the alternative hypothesis suggests it is less than 90% (Hₐ: p < 0.9). Given that the P-value is 0.044 and the significance level (α) is 0.05, we compare the P-value with the significance level to make a decision.

Since the P-value is less than the significance level (0.044 < 0.05), we reject the null hypothesis. This implies that there is sufficient evidence to support the alternative hypothesis, leading to the conclusion that the proportion of responses within 8 minutes is less than 90%. Therefore, the correct answer is option b: We would reject the null hypothesis. This means that on the basis of the evidence, you can conclude that the proportion of responses within 8 minutes is less than 90%.