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A researcher believes that in recent years, marathon runners are getting faster. She knows that 15 years ago, the average finishing time for all runners was 4 hours and 30 minutes with a standard deviation of 3 minutes and 25 seconds. She randomly samples 50 runners from a recent marathon and records their finishing times. What test would the researcher use to test her hypothesis?

Group of answer choices:
1. Dependent Sample T-Test
2. One-Sample T-Test
3. Z-Test
4. It would be impossible to conduct this test.

Answer :

To determine whether recent marathon runners are significantly faster now compared to 15 years ago, the researcher needs to conduct a hypothesis test about the mean finishing time.

Step-by-Step Explanation

  1. Who?

    • The researcher is interested in the population of marathon runners' finish times.

  2. What?

    • The goal is to test if the average finishing time has decreased from the 4 hours and 30 minutes recorded 15 years ago.

  3. Why?

    • To validate if marathon runners are indeed faster in recent years.

  4. How?

    • By using a statistical test to check if the sample mean of the recent 50 marathon runners is significantly different (lesser) than the historical average mean.

  5. Test Choice

    • Given that the sample size is 50, which is sufficiently large, and assuming the population standard deviation is known or close to the sample standard deviation, a Z-Test can be a suitable choice. The Z-Test is generally used when the sample size is large (typically n > 30) and the population standard deviation is known.

  6. Option Chosen

    • Z-Test

Ultimately, the researcher would conduct a one-sided Z-test to assess whether the newer sample data indicates a mean finishing time significantly less than the historical mean of 4 hours and 30 minutes.

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