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 0.100 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

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

H0: μ ≥
H1: μ <

b.	State the decision rule for 0.100 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?

  (Click to select)  Reject or Do not reject  H₀. The cost is  (Click to select)  not less or less  than $10,000.

Answer 1

Mean X̅ = Σ Xi / n
X̅ = 84.7 / 8 = 10.5875
Sample Standard deviation SX = √ ( (Xi - X̅ )2 / n - 1 )
SX = √ ( 15.3291 / 8 -1 ) = 1.4798

Part a)

To Test :-

H0 :- µ >= 10
H1 :- µ < 10

Part b)

Reject null hypothesis if t < -t(α, n-1)
Critical value t(α, n-1) = t(0.1 , 8-1) = 1.415
t < - 1.415

Part c)

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 10.5875 - 10 ) / ( 1.4798 / √(8) )
t = 1.123

Part d)

t > -t(α, n-1) = 1.1229 > - 1.415
Result :- Fail to reject null hypothesis

Do not reject  H0. The cost is not less than $10,000.