Answer:
a) Hypothesis mean differs from 0.5025. Rejected
b) P-value = 0
c) 0.50456 < u < 0.50464
Step-by-step explanation:
Given:
- The standard deviation s.d = 0.0001 in
- The mean of the sample x = 0.5046 in
- Sample size n = 25
Find:
a) Test the hypothesis that mean rod. Assume two-sided alternative and significance level of 0.05.
b) Find the p-value for test in part
c) Construct a 95% two-sided confidence interval on the mean rod diameter.
Solution:
- The random variable X: the measurements for rod diameter follows a normal distribution:
X~ N( 0.5025 , 0.0001 )
- Testing H_o: u_o = 0.5025 , H_1 : u_o not equal 0.5025
- Compute the corresponding Z-score:
Z_o = (0.5046 - 0.5025) / 0.0001/sqrt(25)
Z_o = 105
- The Z score value with respect to significance level is:
Z_a/2 = Z_0.025 = 1.96
Hence, Z_o > Z_a/n
- The hypothesis H_o is rejected the mean differs from 0.5025.
- The corresponding P-Value is:
P-value = 2*(1 - sig(Z_o)) = 2*(1 - sig(105))
P-value = 2*(1-1) = 0
- The confidence interval is:
( x - Z_a/2(s.d/sqrt(n)) < u < ( x + Z_a/2(s.d/sqrt(n))
( 0.5046 - 1.96(0.0001/sqrt(25)) < u < ( 0.5046 + 1.96(0.0001/sqrt(25))
0.50456 < u < 0.50464
