ANSWER THE FOLLOWING PROBLEMS

A. Compute for the test-statistic value.

1.) A pharmaceutical company says that the efficacy rate of their medicine is 90% and the standard deviation is 2%. A sample of 500 volunteers from a city reveals that the efficacy rate is 88% with a standard deviation of 3%. At 1% significance level, check the veracity of the statement of the company.

2.) The average income of a customer service representative is P 23,000. A survey was conducted among 25 customer service representatives in the city and the mean is 24,000 and the standard deviation is P 5,000. Is there a significant difference between the population mean and sample mean at 5% significance level?

3.) A laboratory is conducting a quality control on the amount of active ingredient in a drug. A single dosage of the drug should contain 12 mg of the active ingredient. Thirty random dosages of the drug revealed that the average amount of the active ingredient is 12.1 mg, and the standard deviation is 0.5 mg. Is there enough evidence with 99% confidence level that the average amount of the active ingredient is greater than 12 mg?

4.) A remittance center claims that the average transaction cost of sending money through their remittance center is 3% of the amount. A sample of 20 clients revealed that the mean transaction cost is 3.4% and the standard deviation is 0.5%. Test at 10% significance level whether the transaction fee is higher than the claim of the remittance center.

5.) According to a guidance counselor, an average student spent less than 7 hours each day for school works. A sample of 100 students in a certain school reveals that the mean hours spent of the students is 6.5 hours with a standard deviation of 0.8. Determine whether the claim of the guidance counselor is correct against the population mean of 7 hours with 95% confidence level.