Question

The number of "destination weddings" has skyrocketed in recent years. For example, 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 $30,000. Listed below is a total cost in $000 for a sample of 8 Caribbean weddings. At the 0.01 significance level, is it reasonable to conclude the mean wedding cost is less than $30,000 as advertised?

28.6 28.5 30.1 31.4 28.9 29.6 31.6 29.2

1. State the null hypothesis and the alternate hypothesis. Use a 0.01 level of significance. (Enter your answers in thousands of dollars.)

2. State the decision rule for 0.01 significance level. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

3. Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.

Answer 1

a) Null and alternative hypotheses

Ho : = 30000

H1 : < 30000

Level of significance a = 0.01

b) tCritical for a = 0.01 and d.f = n -1 = 8-1 = 7 , left tailed test

tCritical = t​​​​​​a , n-1 = t​​​​​​0.01 , 7 = -2.998

Decision rule : Reject Ho if t < -2.998 , otherwise fail to reject the null hypothesis

c) t test statistic

t = ( xbar - )/(s/√n)

t = ( 29737.5-30000)/(1207.05/√8)

t = - 0.615

here t = -0.615 > -2.998 , we fail to reject the null hypothesis

Conclusion : There is no sufficient evidence to conclude the mean wedding cost is less than $30,000 as advertised