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.) |
H_{0}: μ ≥ | |
H_{1}: 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 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. |
What is the conclusion regarding the null hypothesis? |
(Click to select) Reject or Do not reject H_{0}. The cost is (Click to select) not less or less than $10,000.
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.
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