Respuesta :
Answer:
We conclude that the mean wedding cost is less than $30,000 as advertised.
Step-by-step explanation:
We are given the following data set:(in thousands)
29100, 28500, 28800, 29400, 29800, 29800, 30100, 30600
Formula:
[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}[/tex] Â
where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations. Â
[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]
[tex]Mean =\displaystyle\frac{236100}{8} = 29512.5[/tex]
Sum of squares of differences = 3408750
[tex]S.D = \sqrt{\frac{3408750}{7}} = 697.82[/tex]
Population mean, μ = $30,000
Sample mean, [tex]\bar{x}[/tex] = $29512.5
Sample size, n = 8
Alpha, α = 0.05
Sample standard deviation, s = $ 697.82
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 30000\text{ dollars}\\H_A: \mu < 30000\text{ dollars}[/tex] We use one-tailed t test to perform this hypothesis.
Formula:
[tex]t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }[/tex]
Putting all the values, we have
[tex]t_{stat} = \displaystyle\frac{29512.5 - 30000}{\frac{697.82}{\sqrt{8}} } = -1.975[/tex]
Now,
[tex]t_{critical} \text{ at 0.05 level of significance, 7 degree of freedom } = -1.894[/tex]
Since, Â Â Â Â Â Â Â Â Â
[tex]t_{stat} < t_{critical}[/tex]
We fail to accept the null hypothesis and reject it.
We conclude that the mean wedding cost is less than $30,000 as advertised.
At the significance level, it is reasonable to conclude the mean wedding cost is less than $30,000 as advertised.
How to explain the significance level?
From the information, the null hypothesis is that the Caribbean wedding was less than $30,000.
The test statistic is -3.813. In this case, since the test statistic is more than -1.895 which is the decision rule, then we won't reject the null hypothesis as the cost is not less than $30000.
Therefore, it can be concluded that the mean wedding cost is less than $30,000 as advertised.
Learn more about significance level on:
https://brainly.com/question/15712887
