Question

A study was conducted by a large cosmopolitan hospital to determine the general public opinion on telemedicine . The hospital management is considering to offer telemedicine if more than three fourths of the general public have a favorable opinion on telemedicine. In a sample of 100 people, 90 declared that they like the idea of telemedicine.

1. What is the parameter of interest and the type of test associated with the hypothesis test testing the validity of the above claim?

2. Calculate the appropriate test statistic, correct up to 3 decimal places.

3. State the critical value(s) associated with a significance level of .01

4. Suppose the calculated test statistic value is 4.5, will you as the hospital statistician convince your management to implement telemedicine?

5. Calculate the minimum sample size to compute a 96% confidence interval of the true proportion of people who would like telemedicine within .01 .

Answer 1

1.

The parameter of interest is the proportion of general public that have a favorable opinion on telemedicine

The hypothesized proportion is 3/4 = 0.75

np(1-p) = 100 * 0.75 * (1 - 0.75) = 18.75

The sample can be assumed to be a random sample and the sample size can be assumed to be less than or equal to 5% of the population size.

Since np(1-p) > 10, the sample size is large enough to approximate the sampling distribution of proportion as normal distribution and conduct a one sample z test.

2.

Standard error of proportion, SE = = 0.0433

Sample proportion, = 90/100 = 0.9

Test Statistic, z = ( - p) / SE = (0.9 - 0.75)/0.0433 = 3.46

3.

Critical value of Z associated with a significance level of .01 is 2.33

4.

Since the calculated test statistic (4.5) is greater than the critical value, we conclude that there is strong evidence that the true proportion of of general public that have a favorable opinion on telemedicine is more than 0.75. Thus, w ae as hospital statistician should convince the management to implement telemedicine.

5.

Z value for 96% confidence interval is  2.054

Margin of error, E = 0.01

Minimum sample size, n =