TOPIC: ESTIMATION OF PARAMETERS

Directions: Solve the following problems. Show your COMPLETE solution.

1.An economist claims that the population standard deviation of the monthly income of all the families who belong t the poverty level is Php2,000. A group of researchers surveyed 300 families who belong to the poverty level ar obtained a mean monthly income of Php5,500. Assuming that the monthly income of the families is approximate normally distributed, find:

a. the point estimate of the population

b. the margin of error if the confidence level is 99% (round off to the nearest hundredths); and

c. the 98% confidence interval of the monthly income of all the families who belong to the poverty level.

2.Teacher Sarah conducted a periodic examination of all of her students enrolled in Statistics and Probability. Th scores are normally distributed with a population standard deviation of 9. Teacher Sarah randomly selected 20 students and obtained a mean score of 75.

a. What is the point estimate of the population mean?

b. Compute the standard error of the mean (round off to the nearest hundredths).

c. At a 90% confidence level, what is the margin of error (round off to the nearest hundredths)?

d. Find the 94% confidence interval for the population mean.

3. An electrical company manufactures light bulbs for LCD projectors with life spans that are approximately normally distributed. A randomly selected sample of 29 lights bulbs has a mean life span of 550 hours with a standard deviation of 45 hours.

a. Compute the margin of error at a 95% confidence level (round off to the nearest hundredths).

b. What is the value of the point estimate?

c. Find the 99% confidence interval for the population mean of all the light bulbs produced by the electrical company.

4.A randomly selected 16 packs of brand X laundry soap manufactured by a well-known company to have contents that are 120g, 122g, 119g, 112g, 123g, 121g, 118g, 115g, 125g, 109g. 108g, 127g, 110g, 120g, 128, and 117g.

a. Compute the margin of error at a 95% confidence level (round off to the nearest hundredths).

b. Compute the value of the point estimate.

c. Find the 90% confidence interval for the mean assuming that the population of the laundry soap content is approximately normally distributed.

5. Based on the results of a survey conducted by a group of researchers, the proportion of females holding executive positions in the government agencies in a certain populated city in the Philippines is normally distributed. In a random sample of 350 female employees in government agencies, 70 female employees hold executive positions.

a. Compute the proportion estimate of the parameter.

b. Compute the margin of error of the proportion at a 90% confidence level (round off to the nearest hundredths).

c. Find the 90% and 98% confidence interval for all the female employees in the government agencies holdi executive positions.