Question

An ambulance service claims that it takes on the average less than 10 minutes to reach its destination in emergency calls. A sample of 36 calls has a mean of 11 minutes and variance 16 minutes. Test the claim at .05 levels Pls Expain the problem step by step process

Answer 1

To test the claim that the average time for the ambulance service to reach its destination is less than 10 minutes, we can use a hypothesis test. If the test statistic falls within the rejection region, we can conclude that there is sufficient evidence to support the claim.

Step-by-step explanation:

To test the claim that the average time for the ambulance service to reach its destination is less than 10 minutes, we can use a hypothesis test.

1. State the null and alternative hypotheses. In this case, our null hypothesis (H0) is that the average time is 10 minutes or more, while our alternative hypothesis (Ha) is that the average time is less than 10 minutes.
2. Calculate the test statistic. We can use the t-distribution since the sample size is small and the population standard deviation is unknown. The test statistic is given by:

   t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

3. Determine the critical value and the rejection region. Since the alternative hypothesis is that the average time is less than 10 minutes, we will use a one-tailed test. Using a significance level of 0.05, the critical value is -1.671.
4. Compare the test statistic to the critical value. If the test statistic is less than the critical value, we reject the null hypothesis. If it is greater, we fail to reject the null hypothesis.
5. Make a conclusion. Based on the calculations, if the test statistic falls within the rejection region, we can conclude that there is sufficient evidence to support the claim that the average time for the ambulance service to reach its destination is less than 10 minutes.