SOLUTION: Hi Tutors, Can u please help me with these problems? 1. A stock of tilapia will only be harvested if the average body weight of the tilapia is greater than 20g. A sample of

Algebra ->  Probability-and-statistics -> SOLUTION: Hi Tutors, Can u please help me with these problems? 1. A stock of tilapia will only be harvested if the average body weight of the tilapia is greater than 20g. A sample of      Log On


   

Question 846439: Hi Tutors,
Can u please help me with these problems?

1. A stock of tilapia will only be harvested if the average body weight of the tilapia is greater than 20g. A sample of 50 pieces is drawn with an average weight of 22g and SD of 15. Using a test of hypothesis at the 1% level of significance, will you decide to harvest your stock?

2. Among 10,000 school children, 500 of them are randomly selected for a survey on nutritional status among school age children. Of these 500 school children, 91 are found to be moderately and severely underweight children. At 5% level of significance, is their evidence that the proportion of moderately and severely underweight children is 20%?

I would truly appreciate it if you can help me.

Thanks,
Shagao
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
1. Assume that the body weight of tilapia, X, is normally distributed.

Null hypothesis: X+%3C=+20
Alternate hypothesis: X+%3E+20

Z score is calculated as: Z+=+%28mu+-+X%29%2F%28S%2Fsqrt%28N%29%29

Critical Z-score is Z%5BCritical%5D+=+%2822+-+20%29%2F%2815%2Fsqrt%2850%29%29+=+0.943

To test the truth of null hypothesis: p%28X+%3C=+20%29+=+p%28Z+%3C=+0.943%29+=+0.827
Since p%28X+%3C=+20%29+%3E+0.01 at 1% significance level the null hypothesis is not true. Hence, I will not decide to harvest the stock.
2. Try yourself following the previous problem. If you need help then contact me.