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 .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.

 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 SX = √ ( (Xi - X̅ )2 / n - 1 )
SX = √ ( 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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