Final answer:
To determine if the microwave company's claim should be rejected, we conduct a hypothesis test to analyze the mean time to pop popcorn. Using a one-sample t-test, we calculate the test statistic and the p-value. Based on the results, we fail to reject the null hypothesis, indicating there is not enough evidence to oppose the company's claim.
Step-by-step explanation:
To determine if the claim that the microwaves can pop popcorn in under 2.25 minutes should be rejected, we will conduct a hypothesis test.
Null Hypothesis (H0): The mean time to pop popcorn is 2.25 minutes or less.
Alternative Hypothesis (Ha): The mean time to pop popcorn is greater than 2.25 minutes.
We will use a one-sample t-test since the population standard deviation is unknown.
Using the information provided, we need to calculate the test statistic and the p-value. The test statistic is calculated as:
t = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))
Plugging in the values, we get t = (2.5 - 2.25) / (0.25 / sqrt(134)) = 2.36.
Using the t-distribution table or calculator, we find that the p-value is greater than 0.05. Therefore, we fail to reject the null hypothesis. The correct answer is C. Fail to reject the null hypothesis. There is not enough evidence to oppose the microwave company's claim.