SOLUTION: Can someone please help me with this question? Thank you. A restaurant that delivers pizza wants to be sure that the delivery times remain consistent regardless of whether they

Question 271285: Can someone please help me with this question? Thank you.
A restaurant that delivers pizza wants to be sure that the delivery times remain consistent regardless of whether they have 1 or 2 delivery drivers working. Use a 0.10 significance level to determine whether or not the mean delivery times for the two different levels of staffing are essentially the same. You may assume the populations are normally distributed and that the samples are independent.
1 Driver 2 Drivers
n1 = 28 n2 = 41
x-bar1 = 19.2 x-bar2 = 23.7
s1 = 5.38 s2 = 5.89
Identify each of the following.
16. The justification for normality in this situation.
17. The null and alternative hypotheses appropriate for this test.(To match the correct answer you will need to take 1 � 2.)
18. The calculated value of the test statistic. (To match the correct answer you will need to take 1 � 2.)
19. The critical-value needed for this test.
20. The decision reached by this test.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A restaurant that delivers pizza wants to be sure that the delivery times remain consistent regardless of whether they have 1 or 2 delivery drivers working.
--------------------
Use a 0.10 significance level to determine whether or not the mean delivery times for the two different levels of staffing are essentially the same. You may assume the populations are normally distributed and that the samples are independent.
1 Driver 2 Drivers
n1 = 28 n2 = 41
x-bar1 = 19.2 x-bar2 = 23.7
s1 = 5.38 s2 = 5.89
Identify each of the following.
16. The justification for normality in this situation.
Normality is assumed.
--------------------------------------------
17. The null and alternative hypotheses appropriate for this test.(To match the correct answer you will need to take 1 � 2.)
Ho: u1 - u2 = 0
Ha: u1 - u2 is not 0
---------------------------------------------
18. The calculated value of the test statistic. (To match the correct answer you will need to take 1 � 2.)
u1-u2 = 5.38-5.89 = -0.51
t(-0.51) = -0.51/sqrt[5.38^2/28 + 5.89^2/41] = -0.3720
--------------------------------------------
19. The critical-value needed for this test.
It's a 2 tail test with alpha = 10% and df = 28+41-2: invT(0.05,67) = -1.6679
--------------------------------
20. The decision reached by this test.
Since test stat is not in the reject interval, fail to reject Ho.
-------------------------------
Cheers,
Stan H.

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