: You and some of your friends have decided to test the validity of an advertise
ID: 3202597 • Letter: #
Question
: You and some of your friends have decided to test the validity of an advertisement by a local pizza restaurant, which says it delivers to the dormitories faster than a local branch of a national chain. Both the local pizza restaurant and the national chain are located across the street from your college campus. The variable of interest is delivery time in minutes from the time the pizza is ordered to when it is delivered. You collect the data ordering 14 pizzas from local pizza restaurant and 14 from the national chain at different times. The following table is the record of the delivery times:
At the .05 level of significance, is there any evidence that the mean delivery time the local pizza restaurant in less than the mean delivery time for the national chain?
Local (Delivery time in minutes)
National Chain (Delivery time in minutes)
16.8
18.1
15.6
16.7
17.5
18.2
19.2
11.7
14.1
21.8
13.9
20.8
21.5
9.8
22.0
15.2
18.7
15.6
20.8
19.7
21.2
19.5
17.0
19.5
16.5
24.0
23.0
24.3
Complete testing in Minitab and prepare report in Word. Enter the data presented above into a Minitab worksheet. Conduct the test with alpha of .05 and complete the following.
Using the six step process for each hypothesis test complete the following for the Pizza Delivery analysis
Set up the six-step process and using an f test determine if the data has equal variances. Include only the critical value and pvalue techniques in your conclusion. Present the Minitab output in your conclusion. For your interpretation discuss whether the distributions have equal variances. Do not include graphs from the f test.
Set In your conclusion present the output from Minitab for:
Critical value/critical ratio technique
pvalue
confidence intervals.
Based on the characteristics of each of the above techniques include statements regarding Fail to reject or rejection of the null and type of error which may have been made.
Interpretation: State whether the variances are significantly different and which type of T test you will undertake given the outcome of the f test you just completed.
Use boxplot to satisfy assumption of normality as sample size is <30. Provide a brief description with the graph as to how normality is or is not supported.
F test and test with boxplot worth 12 points.
T test also called paired t, matched pairs or t test for dependence.
Local (Delivery time in minutes)
National Chain (Delivery time in minutes)
16.8
18.1
15.6
16.7
17.5
18.2
19.2
11.7
14.1
21.8
13.9
20.8
21.5
9.8
22.0
15.2
18.7
15.6
20.8
19.7
21.2
19.5
17.0
19.5
16.5
24.0
23.0
24.3
Explanation / Answer
Given that,
mean(x)=16.8357
standard deviation , s.d1=3.5641
number(n1)=14
y(mean)=19.7857
standard deviation, s.d2 =2.9724
number(n2)=14
null, Ho: u1 = u2
alternate, H1: u1 < u2
level of significance, = 0.05
from standard normal table,left tailed t /2 =1.771
since our test is left-tailed
reject Ho, if to < -1.771
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =16.8357-19.7857/sqrt((12.70281/14)+(8.83516/14))
to =-2.378
| to | =2.378
critical value
the value of |t | with min (n1-1, n2-1) i.e 13 d.f is 1.771
we got |to| = 2.37839 & | t | = 1.771
make decision
hence value of | to | > | t | and here we reject Ho
p-value:left tail - Ha : ( p < -2.3784 ) = 0.0167
hence value of p0.05 > 0.0167,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 < u2
test statistic: -2.378
critical value: -1.771
decision: reject Ho
p-value: 0.0167
we have evidence that the mean delivery time the local pizza restaurant in less than the mean delivery time
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