Question

The mean waiting time at the drive-through of a fast food from the time the order is placed to the time the order is recieved is 84.3 seconds. A manager devises a new drive-through system that he believes will decrease the wait time. To test his claim, he initiates the new system at his restaurant and measures the wait time for 45 randomly selected orders and finds the sample mean to be 81.9 and a sample standard deviation of 17.3.
1. Has the wait time significantly decreased?
2. Write the appropriate hypothesis statements for this test.
3. Also what is the t-test and p-value?

Answer 1

Answer:

1.) No ;

2.) - 0.931

3.) 0.1785

Step-by-step explanation:

Given :

μ = 84.3 ; xbar = 81.9 ; s = 17.3

H0 : μ = 84.3

H1 : μ < 84.3

The test statistic :

(xbar - μ) ÷ (s/√(n))

(81.9 - 84.3) / (17.3/√45)

-2.4 / 2.5789317

= - 0.9306

= - 0.931

Using the test statistic, we could obtain the Pvalue : df = n - 1 ; df = 45 - 1 = 44

Using the Pvalue calculator :

Pvalue(-0.9306, 44) = 0.1785

Using α = 0.05

The Pvalue > α

Then we fail to reject H0; and conclude that there is no significant evidence to support the claim that the mean waiting time is less than 84.3