Confidence Interval and Hypothesis Testing for Population Mean

Part - A – Problems
1

1. Answer:
a. Sample mean
x
−
=745+ 752+ 754+745+748+ 753+746+742+745+748+741+746
12 =747 . 08 ml
Sample standard deviation
s=∑
i=1
12
√ ( xi−747 .08 )
2
12 =4 . 12ml
, where xi s are the sample observations
At 95% confidence level the value of t=2 .20 (two tail)
Population mean = μ=750 ml
Hence, confidence interval is
x
−
±t∗ s
√ n =747 . 08±2. 20∗4 .12
√ 12 =[744 .75 , 749 . 41]
b. Assuming the data to be normally distributed the claim is tested.
Null Hypothesis: H 0 : ( μ=750 )
Alternate Hypothesis: HA : ( μ≠750 )
Let level of significance is 5% and the critical value of the test statistic (t-stat) is
found at (12-1) = 11 degrees of freedom as tcrit =2. 20
2