An engineering company wants to have a hypothesis test on its certain type of products. A quality control engineer measures the strength of 16 sample products of that type, and computes a sample mean equal to 103.6 and sample variance equal to 36.
1. Perform a hypothesis test at significance level equal to 0.05 and analyze the claim that the average strength of this type of products is less than 106.
2. Perform a hypothesis test at significance level equal to 0.05 and analyze the claim that the variance of this type of products is not equal to 30.
Solution:
1. n=16
sample mean=103.6
sample variance=36
α=0.05
null hypo: μ=106
Alternative hy: μ<106
Using test statistics formula i got
Z=-1.6
Then using z score calculator i got p value 0.0548
As it is approximately equals to 0.05 so null hypothesis is rejected. Which means the average strength of this type of products is less than 106 is true.
Have i solved it correctly. If i have made any errors please guide me. It's for part 1.
For part 2:
s²=36
Null hyp: σ²=30
Alternating Hyp: σ²≠30
Using chi square distribution:
I got chi square=18
Then found p value=0.2627 <p
So reject null hypothesis so the true variance of this type of products is not equal to 30.
Is it correct?
Please guide me if i have done something wrong.
Thanks in advance
1. Perform a hypothesis test at significance level equal to 0.05 and analyze the claim that the average strength of this type of products is less than 106.
2. Perform a hypothesis test at significance level equal to 0.05 and analyze the claim that the variance of this type of products is not equal to 30.
Solution:
1. n=16
sample mean=103.6
sample variance=36
α=0.05
null hypo: μ=106
Alternative hy: μ<106
Using test statistics formula i got
Z=-1.6
Then using z score calculator i got p value 0.0548
As it is approximately equals to 0.05 so null hypothesis is rejected. Which means the average strength of this type of products is less than 106 is true.
Have i solved it correctly. If i have made any errors please guide me. It's for part 1.
For part 2:
s²=36
Null hyp: σ²=30
Alternating Hyp: σ²≠30
Using chi square distribution:
I got chi square=18
Then found p value=0.2627 <p
So reject null hypothesis so the true variance of this type of products is not equal to 30.
Is it correct?
Please guide me if i have done something wrong.
Thanks in advance