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:
where
are data points,
is the mean and n is the number of observations.
![Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}](https://tex.z-dn.net/?f=Mean%20%3D%20%5Cdisplaystyle%5Cfrac%7B%5Ctext%7BSum%20of%20all%20observations%7D%7D%7B%5Ctext%7BTotal%20number%20of%20observation%7D%7D)
![Mean =\displaystyle\frac{236100}{8} = 29512.5](https://tex.z-dn.net/?f=Mean%20%3D%5Cdisplaystyle%5Cfrac%7B236100%7D%7B8%7D%20%3D%2029512.5)
Sum of squares of differences = 3408750
![S.D = \sqrt{\frac{3408750}{7}} = 697.82](https://tex.z-dn.net/?f=S.D%20%3D%20%5Csqrt%7B%5Cfrac%7B3408750%7D%7B7%7D%7D%20%3D%20697.82)
Population mean, μ = $30,000
Sample mean,
= $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
We use one-tailed t test to perform this hypothesis.
Formula:
Putting all the values, we have
Now,
Since,
![t_{stat} < t_{critical}](https://tex.z-dn.net/?f=t_%7Bstat%7D%20%3C%20t_%7Bcritical%7D)
We fail to accept the null hypothesis and reject it.
We conclude that the mean wedding cost is less than $30,000 as advertised.