The cost of weddings in the United States has skyrocketed in

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 0.050 significance level is it reasonable to conclude the mean wedding cost is less than $10,000 as advertised?

10.1

9.8

8.8

10.3

9.0

9.7

8.5

8.6

a.

State the null hypothesis and the alternate hypothesis. Use a .05 level of significance. (Enter your answers in thousands of dollars.)

  H0:
  H1: <

b.

State the decision rule for 0.050 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?

H0. The cost is than $10,000.

Solution

a.

H0: $10,000
  H1: < $10,000

b.

Reject H0 if t < - 1.895

c.

Standard Error = 710/sqrt(8) = 250

Test Statistic, t = (9350-10000)/250 = -2.589

d.

Since test statistic is less than critical value we reject the null hypothesis.