The cost of weddings in the United States has skyrocketed in

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 .10 significance level is it reasonable to conclude the mean wedding cost is less than $10,000 as advertised?

10.5

11.6

12.4

8.5

10.1

12.6

9.5

9.5

State the null hypothesis and the alternate hypothesis. Use a .10 level of significance. (Enter your answers in thousands of dollars.)

State the decision rule for .10 significance level. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

Compute the value of the test statistic. (Negative amount should be indicated by a minus sign.Round your answer to 3 decimal places.)

At the .10 significance level is it reasonable to conclude the mean wedding cost is less than $10,000 as advertised?

Solution

Set Up Hypothesis
Null, H0: U<=10
Alternate, H1: U>10
Test Statistic
Population Mean(U)=10
Sample X(Mean)=10.5875
Standard Deviation(S.D)=1.4798
Number (n)=8
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =10.5875-10/(1.4798/Sqrt(7))
to =1.123
| to | =1.123
Critical Value
The Value of |t | with n-1 = 7 d.f is 1.415
We got |to| =1.123 & | t | =1.415
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho

ANS:
H0: U<=10 , H1: U>10
Reject Ho, If < 1.415
to =1.123
Do not Reject Ho
less than $10,000