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.) |
H_{0}: μ ≥ | |
H_{1}: 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 H_{0} 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 H_{0}. The cost is (Click to select)lessnot less than $10,000. |
Values ( X ) | Σ ( X_{i}- 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.
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