Ten new devices were tested under two weather conditions. High wind speeds with
ID: 3339567 • Letter: T
Question
Ten new devices were tested under two weather conditions. High wind speeds with low visibility and Low wind speeds with high visibility. Their accuracies are measured, the measurements of their accuracies are as follows.
A) At the 3% significance level, test if the accuracy of the device is higher at Low wind speed with high visibility than at High wind speed with low visibility condition
B) Find a 90% confidence interval for the difference for the means of the device accuracies.
C) State and check the assumptions needed for the above procedures.
Device
High wind speed with low visibility
Low wind speed with high visibility
1
140
192
2
139
188
3
148
190
4
136
186
5
129
179
6
145
194
7
155
183
8
130
191
10
123
187
Device
High wind speed with low visibility
Low wind speed with high visibility
1
140
192
2
139
188
3
148
190
4
136
186
5
129
179
6
145
194
7
155
183
8
130
191
10
123
187
Explanation / Answer
Here mean and standard deviation of devices in the below given table:
(a) Here confidence level = 0.03
Here, H0 : accuracy of Low wind speed with high visibility is same for High wind speed with low visibility. 1 = 2
Ha : accuracy of Low wind speed with high visibility is more than High wind speed with low visibility. 1 < 2
Here
Test statistic "
t = (x2 - x1)/ sqrt [s12/n1 + s22/n2 ]
t = (187.78 - 138.33)/ sqrt [102/9 + 21.944/9 ]
t = 49.45/ 3.711 = 13.325
Here as varaince are more then 4 times different so we will use t test with unequal varainces
dF = (s12/n1 + s22/n2)2 / [ (s12/n1)2 /(n1 -1)+ (s22/n2)2 /(n2 -1)]
dF = 11
so critical value of t for 0.03 and dF =11
t0.03,11 = 2.096
so here t > t0.03,11 so we shall reject the null hypothesis and can claim that accuracy of Low wind speed with high visibility is more than High wind speed with low visibility.
(b) 90% confidence interval for accuracy = (x2 - x1) +- Z90% sqrt [s12/n1 + s22/n2 ]
= (187.78 - 138.33) +- 1.645 * sqrt [102/9 + 21.94/9]
= 49.45 +- 6.1045
= (43.35, 55.55)
(c) State and check the assumptions needed for the above procedures.
(i) The data must be normally distributed.
(ii) The samples must be randomly drawn.
(iii) Data must not contain otliers.
Device High wind speed with low visibility Low wind speed with high visibility Mean 138.33 187.78 Std.dev. 10.10 4.68Related Questions
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