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 0.10 significance level, is it reasonable to conclude the mean wedding cost is less than $30,000 as advertised? 30.3 30.0 28.8 30.1 31.9 29.2 29.4 28.5

A. State the null hypothesis and the alternate hypothesis. Use a 0.10 level of significance. (Enter your answers in thousands of dollars.)

B. State the decision rule for 0.10 significance level. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

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

D. What is the conclusion regarding the null hypothesis? _________(reject/do not reject) H0. The cost is _________ (not less/less) than $30,000

Answer 1

(a)  

Ho:

Ha:

Null hypothesis states that the cost of a Caribbean wedding is equal to $30,000.

Null hypothesis states that the cost of a Caribbean wedding is less than $30,000.

(b) Level of significance = 0.10

n = 8-1 = 7

t value (left tailed) = -1.415

(c) Test statistics

mean = sum of all terms / no of terms = 238.2 / 8 = 29.775

sample mean = 29775

standard deviation = s

data	data-mean	(data - mean)2
30.3	0.525	0.275625
30.0	0.225	0.050625000000001
28.8	-0.975	0.950625
30.1	0.325	0.105625
31.9	2.125	4.515625
29.2	-0.575	0.330625
29.4	-0.375	0.140625
28.5	-1.275	1.625625

s = 1.0687 * 1000 = 1068.70

Assuming data is normally distributed and as population sd is not given, we will calculate t stat

t stat = -0.595

(d) As the t stat (-0.595) does not fall in the rejection area, we fail to reject the Null hypothesis.

Hence we do not have sufficient evidence to believe that cost of a Caribbean wedding is less than $30,000.