Question

A researcher wishes to estimate with 95% confidence the proportion of adults who have high speed internet access. Her estimate must be accurate within 4% of the true proportion.
1. Find the minimum sample size needed using a prior study that found that 48% of the respondents said they have high speed internet access
2. No preliminary estimate is available. Find the minimum sample size needed.

Answer 1

Formula to find sample size:
n = [(z-value)^2 * p * q]/E^2
... where n = sample size, z-value is found using a z-table for 95% confidence, p = .48, q = 1 - p, ^2 means squared, * means to multiply, and E = .04 (or 4%).

For 2): use p = .5 (when no value is stated in the problem), q = 1 - p

I hope this will help get you started.

Answer 2

1) A group of scientists created 150 trials to measure whether electric shock treatment could cure paranoid delusions. Of these trials, 52 were successful. Find the margin of error E that corresponds to a 95% confidence level. The critical value for 95% confidence level is 1.96.

2) Find the minimum sample size that should be chosen to assure that the proportion estimate p will be within the required margin of error, .06. Use a 95% confidence interval and a population proportion of .7. The critical value for a 95% confidence level is 1.96

3) Find the test statistic for the following proportion: A collection of 500 randomly selected teachers revealed that 61% felt that all students should be required to take algebra in high school.

4) Employees in a large computer firm claim that the mean salary of the firm™s programmers is less than that of its competitors. The competitor™s salary is $47,000. A random sample of 30 of the firm™s programmers has a mean salary of $46,500 with a standard deviation of 5500. Calculate the test statistic for the hypothesis: Ho: mean >= 47000, H1: mean < 47000

Answer 3

Find the minimum sample size that should be chosen to assure that the proportion estimate p will be within the required margin of error, .06. Use a 95% confidence interval and a population proportion of .7. The critical value for a 95% confidence level is 1.96

Find the test statistic for the following proportion: A collection of 500 randomly selected teachers revealed that 61% felt that all students should be required to take algebra in high school.

Employees in a large computer firm claim that the mean salary of the firm™s programmers is less than that of its competitors. The competitor™s salary is $47,000. A random sample of 30 of the firm™s programmers has a mean salary of $46,500 with a standard deviation of 5500. Calculate the test statistic for the hypothesis: Ho: mean >= 47000, H1: mean < 47000