Question

In: Math

1. Use the diamond data: Is there enough evidence in the data that population average price...

1. Use the diamond data:

Is there enough evidence in the data that population average price of diamond for color “E” is more than 1500.

Please solve using R please.

Thank you

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

Solutions

Expert Solution

Soln

data_5Nov = read.csv(file.choose(),header = T)

head(data_5Nov)

Output

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")
Output
        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.


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