Expert: Chen Min - 1/19/2011

Question
Hi Mr.chen, i need your help,im a 2nd student for answering this 6 problem, this are my assignment, please answer it... im also trying hard to answer it but its very hard for me.... Thanks for advance.

1.   A stock of tilapia will only be harvested if the average of tilapia is greater than 20 grams. A sample of 50 pcs is drawn with an average weight of 22 grams. And a standard deviation of 15 grams. Using a testing of hypothesis at a 1% level of significance will you decide to harvest your stock?
2.   A poll survey in Metro Manila was conducted right after EDSA 2 in order to determine what percentage of the voting population you would still vote for Estrada for the next election the results of the survey revealed that out of 88 respondents certified would still vote for President Erap. At a 5% level of significance is their evidences that the proportion of voters that would still estimate would exceed 40%.
3.   According to the results of 1998 national demographic survey of NSO, out of 11059 women age 20-49 years old, 288 had sexual intercourse by age of 15. Using a 5% level of significance is there enough evidence that the proportion of women 20-49 years old who had sexual intercourse by age 15 would exceed 3%.
4.   In a study of factors affecting hypertension, visual analog scale sensory ratings where obtained for 16 subjects. For these sample ratings the mean is 8.33 while the standard deviation is 1.96 at a 1% level of significance, test determined that these sample comes from a population with a mean rating of less than 10.
5.   In a study of a store checkout scanner, 1234 items were checked and 20 of them were found to be overcharges. Use a 5% level of significance to test the claim that with the scanners 1% sales are overcharges. Based on these results, do scanners appear to have consumers avoid overcharges?
6.   Ms. Abad Santos is a high school history teacher who says that each student is not aware of the martial law then the Curriculum should be revised to correct that depraving. A survey of 506 student’s high school showed that 268 of them did not know that the Philippines were under the Martial Law for more than 10 years. Using the sample data and a 5% level of significance, test determined that students do not know what happened during the martial law. Based on these results, should Ms. Abad Santos seek revision to the curriculum?


Take care and good health

Answer
This needs a lot of work with GC / Distribution table, besides it's homework, so I'll just give you directions for each qns.

1.You don't know what's the distribution type of the pcs sampled, but since the sample size (50) is large, you can approximate the sample mean as varying normally by Central Limit Theorem, with mean 22 and SD 15/sqrt50. Then you can use a z-test to see the p value under null hypothesis (that stock can be harvested). Alternatively, you draw out the sample mean distribution and calculate if P(sample mean<20) < 1%, if not, then the null hypothesis must be rejected.

2.I think something is missing...how many would still vote out of 88?

3.This question is hard because it does not give a scent of distribution, so you'll have to devise one. Assume the probability of a randomly chosen woman turns out 'coitused' is p, hence for a population n, the total number of 'coitused' women (X)obey binomial distribution X~B(n,p);For a sample size large enough this is approximated to normal X~(np, np(1-p)), you should know this. Then, for any specific sample of size n, the distribution of sample mean also follows ND, meanX~(np,p(1-p)/n). Sub in p=0.03 and n=11059 and see where 288 lies.

4.Since sample size is small and does not necessarily follow normal dist, you'll have to use a t-test. The detail of which I won't go further, just punch the values into GC and get your p value.

5.Sample size large, Central Limit Theorem approximation to normal, and use z-test.

6.I really don't understand the qn...sorry...does it mean curriculum needs revision only when EVERY student does not know Philippine Martial Law thingy? That's absurd..

Hope you find this helpful