Question

Select two data values from your raw data – one that is inside of the confidence interval and one that is outside – one must be at the high end of the data and one at the low end – and construct two hypothesis tests, one for each value. One of the tests should be a “less than”, the other should be a “greater than”, depending on the value being tested. Use a 95% level of confidence.

Songs
250
5
800
500
850
430
200
600
0
130
1000
1000
400
1500
20
1500
872
150
115
90
252
2345
200
200
300
200
650
1500
600
500
800
400
930
400
10000
456
200
1200
0
500
30
0
950
180
450
1000
730
10
10
55
260
500
0
1327
0
250
0
35
100
1000
10
35
0
1200
2000
200
1813
15
90
5
100
300
1400
200
22
800
300
1000
15
75
200
700
167
200
183
678
50
350
150
400
2000
2000
900
1
400
300
100
150
300
150
100
1200
1500
200
100
1500
300
300
3000
2000
150
100
200
4000
200
500
1500
500
3600
1567
350
181
400
500
0
250
100
50
300
300
500
2000
60
200
0
100
350
400
1000
40
250
1750
0
0
400
840
200
300
500
0
800
200
400
15
45
170
150
0
2409
350
2100
200
200
25
25
0
200
0
0
1200
450
400
2750
300
300
1869
970
300
2900
1140
40
100
2000
500
1000
0
500
30
0
500
812
0

Answer 1

We first test a two side test to determine the confidence interval. The confidence interval is found to be (467.7,752.2)

Then we choose a lower end value inside this confidence interval. Say 500 among th raw data and perform "greater than" alternative hypothesis test.

Then we choose a higher end data say, 3600 among the raw data ehich is outside the confidence interval and perform "less than" alternative hypothesis test.

conclusion for the lower end test : p value =0.065>0. 05 so we accept null hypothesis and conclude there is no significant difference in the mean. (hypothesised mean=500)

Conclusion for the higher end test : p value =0<0.05 so we reject null and conclude there is significant difference in the mean. (hypothesised mean=3600)