werson9339 said:Homework Statement
This involve testing population proportion. (either small or big sample) this question is done by my lecturer by using binomial , i am wondering could it be done using normal distribution? because the np is 20(0.45) = 9 which is greater than 5 , https://www.flickr.com/photos/110120...6/15432962168
Homework Equations
The Attempt at a Solution
Binomial population proportion testing is used when the sample size is small and the population standard deviation is unknown. It assumes that the data follows a binomial distribution. Normal population proportion testing is used when the sample size is large and the population standard deviation is known. It assumes that the data follows a normal distribution.
The test statistic for binomial population proportion testing is calculated using the formula z = (p̂ - p0) / √(p0(1-p0)/n), where p̂ is the sample proportion, p0 is the hypothesized population proportion, and n is the sample size. For normal population proportion testing, the test statistic is calculated using the formula z = (p̂ - p0) / √(p0(1-p0)/n), where p̂ is the sample proportion, p0 is the hypothesized population proportion, and n is the sample size.
The critical value for binomial population proportion testing can be found using a binomial distribution table or calculated using the formula zα/2 = ± invNorm(α/2), where α is the significance level. For normal population proportion testing, the critical value can be found using a normal distribution table or calculated using the formula zα/2 = ± invNorm(α/2), where α is the significance level.
The purpose of conducting binomial or normal population proportion testing is to determine whether a sample proportion is significantly different from a hypothesized population proportion. This can help researchers make conclusions about a population based on a sample.
A one-tailed test is used to determine if the sample proportion is significantly greater than or less than the hypothesized population proportion. A two-tailed test is used to determine if the sample proportion is significantly different from the hypothesized population proportion in either direction. The choice between a one-tailed or two-tailed test should be based on the research question and hypothesis being tested.