English Celts 141 133 148 138 132 130 138 138 154 134 142 127 150 128 146 138 15
ID: 3245789 • Letter: E
Question
English
Celts
141
133
148
138
132
130
138
138
154
134
142
127
150
128
146
138
158
136
150
131
140
126
147
120
148
124
144
132
150
132
149
125
If a difference is found, produce the appropriate confidence interval for the difference between the population means to go along with the one-tailed test of hypothesis. Show the formula and your calculations.
English
Celts
141
133
148
138
132
130
138
138
154
134
142
127
150
128
146
138
158
136
150
131
140
126
147
120
148
124
144
132
150
132
149
125
( = .10)Explanation / Answer
H0 : average head breath of english is less or same to average head breath of celts. english <= celts
Ha ; Average head breath of english is greater than the average head breath of celts. english > celts
alpha = 0.10
HEre
Pooled Standard deviation sp = sqrt [ (6.40282 + 5.43452 )/2] = 5.9384
standard error of difference sed = sp sqrt (2/n) = 5.9384 * sqrt (2/16)= 2.1000
so Test Statistic
t = (xEnglish - xCelts )/ sed = (146.0625 - 130.75)/ 2.10 = 7.29
p - value = 2 x 10-8
critical value of t for dF = 30 and alpha = 0.10 for one direction is t = 1.697
so t > tcritical
so we can reject the null hypothesis and can say that average breath size of english heads are more than celts heads.
We can solve it by confidence interval method too. we will use one sided confidence interval because it is one direction test.
Here the 95% confidence interval for difference = (xenglish head - x celt head) +- t30,0.10 (sed)
= (146.0625 - 130.75) - 1.697 * 2.1000
= 15.3125 - 3.5637 = 11.75
so confidence interval is (11.75, infinity)
so the confidence interval doesn't consists zero so we can reject the null hypothesis .
English Celts 141 133 148 138 132 130 138 138 154 134 142 127 150 128 146 138 158 136 150 131 140 126 147 120 148 124 144 132 150 132 149 125 Average 146.0625 130.75 Std. Dev. 6.4028 5.4345Related Questions
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