Question

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

Solve in R using the t test.

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

Answer 1

####Import the given file from Excel to R#####
>library(readxl)
>t_test <- read_excel("C:/Users/Admin/Desktop/t_test.xlsx")
>View(t_test)

####Now to extract the rows for E########
>install.packages("dplyr")
>library(dplyr)
>t=t_test %>% filter(Color=="E")

#######Performing t-test######
###Null Hypothesis: Mean=1200
###Alternate: Mean>1200
#### At 95% level of sognificance

>t.test(t$Price, mu=1500, alternative="greater",conf.level = 0.95)

Results from R is given as-

Based on the above results we have

t = 4.75, df = 15, p-value = 0.000129

since the p-value is less than 0.05(alpha value), therefore we have enough evidence to reject the null hypothesis that the average price of diamond for color “E” is more than 1500.

Thanks