1 answer

Statistics

Question:

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


Answers

Given that The MacBurgerrestaurant chain claims that the waiting time of customers forservice is normally distributed,with a mean of3(μ) minutes anda standard deviation of 1(σ)minute. The quality-assurance departmentfound in a sample of 50(n) customers at the Warren Road MacBurgerthat the mean waiting time was 2.75(x-bar)minutes.
Null Hypothesis:
μ=3
Alternative Hypothesis:μ<3
The test statistic is given by

Substitute the values we have

= -1.7678
The critical value of 'z' at 0.05 is 1.645
Since the calculated value of |z| is greater than the criticalvalue of 'z' so we reject the null hypothesis and conclude thatthe mean waiting time is less than3 minutes
Hope this will help you
.

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