A pizza delivery chain advertises that it will deliver your pizza in 2020 minutes from when the order is placed. Being a skeptic, you decide to test and see if the mean delivery time is actually more than 2020 minutes. For the simple random sample of 1414 customers who record the amount of time it takes for each of their pizzas to be delivered, the mean is 22.622.6 minutes with a standard deviation of 5.05.0 minutes. Assume that the population distribution is approximately normal. Perform a hypothesis test using a 0.0050.005 level of significance.

Step 1 of 3 :  

State the null and alternative hypotheses for the test. Fill in the blank below.


H0Ha: μ=20: μblank20


In this hypothesis test, we are checking whether the mean delivery time is actually greater than 20 minutes, as opposed to the chain's claim of delivering within 20 minutes. 

### Step 1: State the null and alternative hypotheses

- The **null hypothesis (H₀)**: The mean delivery time is **20 minutes**, which aligns with the company's claim.
  
  \[
  H_0: \mu = 20
  \]

- The **alternative hypothesis (Hₐ)**: The mean delivery time is **greater than 20 minutes** (since you are testing whether it's more than the claimed 20 minutes).
  
  \[
  H_a: \mu > 20
  \]

These hypotheses will be used for the hypothesis test.

Let me know if you'd like to proceed with the next step or need any clarification!

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### Related Questions:

1. What kind of test statistic would be used in this scenario?
2. Why do we assume the population is normally distributed for this test?
3. How does the sample size affect the reliability of this hypothesis test?
4. What does the significance level of 0.005 imply in terms of rejecting the null hypothesis?
5. What are the possible outcomes of this hypothesis test?

### Tip:
In hypothesis testing, if the p-value is less than the significance level, you reject the null hypothesis in favor of the alternative hypothesis.

A pizza delivery chain advertises that it will deliver your pizza in 20 minutes from when the order is placed. Being a skeptic, you decide to test and see if the mean delivery time is actually more than 20 minutes. For the simple random sample of 14 customers who record the amount of time it takes for each of their pizzas to be delivered, the mean is 22.6 minutes with a standard deviation of 5.0 minutes. Assume that the population distribution is approximately normal. Perform a hypothesis test using a 0.005 level of significance. State the null and alternative hypotheses for the test.

Explore a hypothesis test on whether pizza delivery times exceed the advertised 20 minutes. Using a sample of 14 customers, the mean delivery time is 22.6 minutes with a standard deviation of 5.0 minutes. Learn about hypothesis testing, z-tests, and significance levels in this detailed solution.

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