In: Statistics and Probability
Find a real-world business example with data set (or example from a case study) and comment on the way hypothesis testing can be applied to answer a relevant business question. Identify the question(s) in your post and provide the data set at an attachment as a reference. please try to do it with R.
Problem Statement
Is there enough evidence in the data that population average price of diamond for color “E” is more than 1500.
Dataset:
Color |
Price |
D |
1302 |
E |
1510 |
G |
1510 |
G |
1260 |
D |
1641 |
E |
1555 |
F |
1427 |
G |
1427 |
H |
1126 |
I |
1126 |
F |
1468 |
G |
1202 |
E |
1327 |
I |
1098 |
E |
1693 |
F |
1551 |
G |
1410 |
G |
1269 |
H |
1316 |
H |
1222 |
E |
1738 |
F |
1593 |
G |
1447 |
H |
1255 |
F |
1635 |
H |
1485 |
F |
1420 |
H |
1420 |
F |
1911 |
H |
1525 |
F |
1956 |
H |
1747 |
I |
1572 |
E |
2942 |
G |
2532 |
E |
3501 |
E |
3501 |
F |
3501 |
F |
3293 |
G |
3016 |
F |
3567 |
G |
3205 |
D |
3490 |
E |
3635 |
F |
3635 |
F |
3418 |
D |
3921 |
F |
3701 |
F |
3480 |
G |
3407 |
E |
3767 |
F |
4066 |
E |
4138 |
F |
3605 |
G |
3529 |
F |
3667 |
I |
2892 |
G |
3651 |
G |
3773 |
F |
4291 |
E |
5845 |
G |
4401 |
G |
4759 |
H |
4300 |
F |
5510 |
G |
5122 |
H |
5122 |
I |
3861 |
F |
5881 |
F |
5586 |
F |
5193 |
H |
5193 |
F |
5263 |
I |
5441 |
I |
4948 |
H |
5705 |
F |
6805 |
H |
6882 |
H |
6709 |
I |
6682 |
E |
3501 |
G |
3432 |
F |
3851 |
H |
3605 |
E |
3900 |
H |
3415 |
H |
4291 |
E |
6512 |
E |
5800 |
F |
6285 |
Soln
data_5Nov = read.csv(file.choose(),header = T)
head(data_5Nov)
Color Price
1 D 1302
2 E 1510
3 G 1510
4 G 1260
5 D 1641
6 E 1555
data = data_5Nov[data_5Nov$Color=="E",] ## to get only the ‘E’ Color records
Alpha = 0.05
Null and Alternate Hypothesis
H0: µ = 1500
Ha: µ > 1500
t.test(data$Price, mu = 1500,alternative = "greater") One Sample t-test
data: data$Price
t = 4.75, df = 15, p-value = 0.000129
alternative hypothesis: true mean is greater than 1500
95 percent confidence interval:
2717.118 Inf
sample estimates:
mean of x
3429.062
Result
Since the p-value is less than 0.05, we reject the null hypothesis in favour of alternate hypothesis.
Conclusion
Population average price of diamond for color “E” is more than 1500.