Hypothesis test Use the 2016 data in this tab and the matching survey data in th
ID: 3320743 • Letter: H
Question
Hypothesis test
Use the 2016 data in this tab and the matching survey data in the Average Customer Visit tab to perfom a hypothesis test to see if both surveys are from the same population with the same mean. It sounds silly but as the business grows it is possible that the customer base(population) could change.
Use the following hypotheses for your test.
H0: 2016 average=2017 average
Ha: 2016 average 2017 average
Since no population standard deviation data is available use the sample standard deviation from 2016.
Below is the customer visit survey data from 2016. Use the data in the Average Customer Visit tab along with this to test the Hypothesis both surveys were from the same population (this seems silly but growing customer base would change the population) Use HO: 2017 population average visits 2016 population average visits Ha: 2017 population average visits not equal to 2016 average visits Remember that there is no inequality in the hypothesis equations so the test will be two sided Data Coming Visits per year Response count 52 2 8 1% 1 Average use assumption 2016 avg the population confidence Critical T Z Stat pg318 in bookExplanation / Answer
Given that,
mean(x)=19.333
standard deviation , 1 =23.9137
number(n1)=6
y(mean)=4.8333
standard deviation, 2 =4.8339
number(n2)=6
null, Ho: u1 = u2
alternate, H1: 1 != u2
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic (z) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
zo=19.333-4.8333/sqrt((571.86505/6)+(23.36659/6))
zo =1.456
| zo | =1.456
critical value
the value of |z | at los 0.05% is 1.96
we got |zo | =1.456 & | z | =1.96
make decision
hence value of | zo | < | z | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 1.456 ) = 0.14546
hence value of p0.05 < 0.14546,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: 1 != u2
test statistic: 1.456
critical value: -1.96 , 1.96
decision: do not reject Ho
p-value: 0.14546
we do not have enough evidence to support the claim
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