Question

# The cost of weddings in the United States has skyrocketed in recent years. As a result,...

 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.

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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