statistics

posted by .

The MacBurger restaurant chain claims that the waiting time of customers for service is
normally distributed, with a mean of 3 minutes and a standard deviation of 1 minute. The
quality-assurance department found in a sample of 50 customers at the Warren Road
MacBurger that the mean waiting time was 2.75 minutes. At the .05 significance level, can
we conclude that the mean waiting time is less than 3 minutes?

  • statistics -

    You can use a one-sample z-test on this data.

    Null hypothesis:
    Ho: µ = 3 -->meaning: population mean is equal to 3 minutes
    Alternate hypothesis:
    Ha: µ < 3 -->meaning: population mean is less than 3 minutes

    Using the z-test formula to find the test statistic:
    z = (sample mean - population mean)/(standard deviation divided by the square root of the sample size)
    z = (2.75 - 3)/(1/√50)

    I'll let you finish the calculation.

    Check a z-table for your critical or cutoff value at .05 level of significance for a one-tailed test (the alternate hypothesis is showing a specific direction; therefore, the test is one-tailed). Compare the test statistic you calculated to the critical value from the table. If the test statistic exceeds the critical value, reject the null and conclude that the mean waiting time is less than 3 minutes. If the test statistic does not exceed the critical value from the table, you cannot reject the null and conclude a difference.

    I hope this will help.

  • statistics -

    .0384

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. statistics

    The time it takes to give a man a shampoo and haircut is normally distributed with a mean of 22 minutes and standard deviation of 3 minutes. Customers are scheduled every 30 minutes. (a) What is the probability that a male customer …
  2. statistic

    The amount of time a bank teller spends with each customer has a population mean of 3.10 minutes and standard deviation of 0.40 minute. If a random sample of 16 customers is selected, a) what assumption must be made in order to solve …
  3. statistics

    Suppose 100 randomly selected customers were asked to rate a particular service they recently had on a scale of 0 to 10. The sample mean rating was found to be 7.3. (Assume the population standard deviation of all ratings in the population …
  4. statistics

    Suppose 100 randomly selected customers were asked to rate a particular service they recently had on a scale of 0 to 10. The sample mean rating was found to be 7.3. (Assume the population standard deviation of all ratings in the population …
  5. Statistics

    A hospital claims that the mean waiting time at its emergency room is 25 minutes. A random sample of 16 patients produced a mean wait time of 27.5 minutes with a standard deviation of 4.8 minutes. Use the 1% level of significance to …
  6. math

    A bank wishing to determine the average amount of time a customer must wait to be served took a random sample of 100 customers and found that the mean waiting time was 7.2 minutes. Assuming that the population standard deviation is …
  7. Statistics

    Service times for customers at a post office follow some right-skewed distribution with mean 2.91 minutes and standard deviation 1.74 minutes. (a) Can you calculate the probability that the average service time for the next two customers …
  8. statistics

    A cell phone service provider has selected a random sample of 20 of its customers in an effort to estimate the mean number of minutes used per day. The results of the sample included a sample mean of 34.5 minutes and a sample standard …
  9. statistics

    historically, the average customer spends $8.53 for all TGP restaurants(u=8.53). If the population standard deviation is $1.06(o=1.06) and the data is normally distributed, find the probabiltiy that the sample mean will be within $.15 …
  10. Statistics (Math 210)

    Hi there, I am working on a few homework assignments and having trouble with a few questions. I sincerely appreciate any and all help! :) A bank claims that the mean waiting time in line is less than 4.1 minutes. A random sample of …

More Similar Questions