The cost of weddings in the United States has skyrocketed in recent years. As a
ID: 3307153 • Letter: T
Question
The cost of weddings in the United States has skyrocketed in recent years. As a result, many couples are opting to have their weddings in the Caribbean. A Caribbean vacation resort recently advertised in Bride Magazine that the cost of a Caribbean wedding was less than $10,000. Listed below is a total cost in $000 for a sample of 8 Caribbean weddings. At the 0.050 significance level is it reasonable to conclude the mean wedding cost is less than $10,000 as advertised? 9.1 9.5 10.1 8.8 8.5 10.1 9.8 9.2 a. State the null hypothesis and the alternate hypothesis. Use a .05 level of significance. (Enter your answers in thousands of dollars. HINT: This means the units are thousands, not ones. If you paid a $5000 bill, how many $1000 bills would you need? If you paid the same bill in $1 bills, how many $1 bills would you need? Make sure you use the correct units.) H0: H1: < b. State the decision rule for 0.050 significance level. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.) Reject H0 if t < c. Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.) Value of the test statistic d. What is the conclusion regarding the null hypothesis? H0. The cost is than $10,000.
Explanation / Answer
Given that,
population mean(u)=10
sample mean, x =9.3875
standard deviation, s =0.5915
number (n)=8
null, Ho: >10
alternate, H1: <10
level of significance, = 0.05
from standard normal table,left tailed t /2 =1.895
since our test is left-tailed
reject Ho, if to < -1.895
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =9.3875-10/(0.5915/sqrt(8))
to =-2.929
| to | =2.929
critical value
the value of |t | with n-1 = 7 d.f is 1.895
we got |to| =2.929 & | t | =1.895
make decision
hence value of | to | > | t | and here we reject Ho
p-value :left tail - Ha : ( p < -2.9288 ) = 0.01103
hence value of p0.05 > 0.01103,here we reject Ho
ANSWERS
---------------
a.
null, Ho: =10
alternate, H1: <10
c.
test statistic: -2.929
critical value: -1.895
decision: reject Ho
p-value: 0.01103
we have evidence that the cost is less than $10,000.
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