The manager of a grocery store has taken a random sample of 100 customers to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. She observes that the average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minutes.
Question
The manager of a grocery store has taken a random sample of 100 customers to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. She observes that the average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minutes.
Solution
It seems like you haven't asked a specific question related to the scenario you provided. However, I can guide you on how to perform a hypothesis test based on the information given.
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State the Hypotheses: The null hypothesis would be that the mean waiting time is equal to 3 minutes. The alternative hypothesis would be that the mean waiting time is more than 3 minutes.
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Choose the Significance Level: Usually, a significance level (denoted as α) of 0.05 works well which means your output should be 95% confident to give a conclusion of the hypothesis.
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Calculate the Test Statistic: Since we know the population standard deviation, we can use the z-test. The formula for the test statistic in a z-test is (X - μ) / (σ/√n), where X is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
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Make a Decision: Compare the test statistic to the critical value from the z-table (based on your chosen significance level). If the test statistic is greater than the critical value, reject the null hypothesis.
Please let me know if you need help with any specific part of this process.
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