Hi to everyone in this forum, I'm a college student having trouble with statistics and have a final exam in 2 days, so can someone please help me out.

-Here is the question and what I came up with...

A fast-food restaunrat advertises that their delivery time is less as compared to a national fast-food chain. To determine whether this advertisement is valid, 10 orders are placed to each restaurant. Delivery time in minutes are shown below:

Local 16.8 11.7 15.6 16.7 17.5 18.1 14.1 21.8 13.9 20.8
Chain 22 15.2 18.7 15.6 20.8 19.5 17 19.5 16.5 24

At the 0.05 level of significance, is there evidence that the mean delivery time is lower for the local pizza restaurant than that of the national pizza chain?


Test Hypothesis

Step1

RV X: Delivery time.
Population 1 - N(u1, varinace(squared)
Sample 1-(X1,s1(squared)

Population 2- N(u2, variance(squared)
Sample 2-(X2,s2(squared)

Step 2

Ho=U1=U2 (mean delivery time for population is same)
H1:U1<U2 (mean delivery time for local pizza restaurant is less than that of the national pizza chain)

Step 3

n (sample size)= 10
x=find it.



Local Chain D=x1-x2 D(squared)
1 16.8 22 -5.2 27.04
2 11.7 15.2 -3.5 12.25
3 15.6 18.7 -3.1 9.61
4 16.7 15.6 1.1 1.21
5 17.5 20.8 -3.3 10.89
6 18.1 19.5 -1.4 1.96
7 14.1 17 -2.9 8.41
8 21.8 19.5 2.3 5.29
9 13.9 16.5 -2.6 6.76
10 20.8 24 -3.2 10.24
Total -21.8 93.66


Mean=21.8/10=2.18

Variance=1/9(93.66-(21.8)squared/10

Variance=5.126

Standard deviation=2.264

Step 4-Test statistic:

T=T/SD/ √n...T=2.18/2.264/3.162= 3.045- The T-value.

Step 5

0.95

1-0.95=0.05
0.05/2=0.025

Corresponding T- value i found from table is 2.2622 (t-value)


So this is what I came up with, How can i come up with a decision on this question.

Thanks....