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

8.6

8.5

12.4

10.5

9.5

8.6

9.4

9.4

(a)	State the null hypothesis and the alternate hypothesis. Use a .05 level of significance. (Enter your answers in thousands of dollars.)

H0: μ ≥
H1: μ <

(b)	State the decision rule for .05 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)	At the .05 significance level is it reasonable to conclude the mean wedding cost is less than $10,000 as advertised?

  (Click to select)Do not rejectReject H₀. The cost is (Click to select)lessnot less than $10,000.

Answer 1

	Values ( X )	Σ ( Xi- X̅ )2
	8.6	1.0252
	8.5	1.2377
	12.4	7.7702
	10.5	0.7877
	9.5	0.0127
	8.6	1.0252
	9.4	0.0452
	9.4	0.0452
Total	76.9	11.9491

Mean X̅ = Σ Xi / n
X̅ = 76.9 / 8 = 9.6125
Sample Standard deviation S_X = √ ( (Xi - X̅ )² / n - 1 )
S_X = √ ( 11.9491 / 8 -1 ) = 1.3065

Part a)

H0 :- µ >= 10
H1 :- µ <= 10

Part b)

Test Criteria :-
Reject null hypothesis if t < -t(α, n-1)
Critical value -t(α, n-1) = -t(0.05 , 8-1) = -1.895

Part c)

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 9.6125 - 10 ) / ( 1.3065 / √(8) )
t = -0.839

Part d)

t > -t(α, n-1) = -0.8389 > - 1.895
Result :- Fail to reject null hypothesis

Do not reject H0, there is insufficient evidence to support the claim that the cost of a Caribbean wedding was less than $10,000.