The number of "destination weddings" has skyrocketed in recent years. For example, many couples are opting to have their wedding

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The number of "destination weddings" has skyrocketed in recent years. For example, many couples are opting to have their wedding

s 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 0.05 significance level, is it reasonable to conclude the mean wedding cost is less than $30,000 as advertised? 29.128.528.829.429.829.830.130.6

Mathematics

1 answer:

zzz [12.3K] · Answer 1 · 2026-03-07T10:00:06+03:00

Answer:

Based on the findings, we infer that the average cost of a wedding is lower than the $30,000 that was initially suggested.

Step-by-step explanation:

The following data set is provided: (in thousands)

29100, 28500, 28800, 29400, 29800, 29800, 30100, 30600

Formula:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where $x_i$ denotes data points, $\bar{x}$ represents the mean, and n indicates the number of samples.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{236100}{8} = 29512.5$

The sum of squares of the differences equals 3408750

$S.D = \sqrt{\frac{3408750}{7}} = 697.82$

The population mean, μ = $30,000

The sample mean, $\bar{x}$ = $29512.5

Sample size, n = 8

Alpha, α = 0.05

Sample standard deviation, s = $697.82

Initially, we formulate the null hypothesis and the alternative hypothesis.

$H_{0}: \mu = 30000\text{ dollars}\\H_A: \mu < 30000\text{ dollars}$ A one-tailed t-test will be conducted for this analysis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

$t_{stat} = \displaystyle\frac{29512.5 - 30000}{\frac{697.82}{\sqrt{8}} } = -1.975$

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$t_{critical} \text{ at 0.05 level of significance, 7 degree of freedom } = -1.894$

$t_{stat} < t_{critical}$

Thus, we conclude that the average wedding cost is indeed less than the advertised $30,000.

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