Consider a binomial experiment with 520 trials and 200 successes. To construct a test for a proportion p, what value do we use for the sample test statistic? Round your answer to two decimal places.
To construct a test for a proportion, we use the sample proportion as the test statistic.
The sample proportion, denoted as p̂ (pronounced "p-hat"), is calculated by dividing the number of successes by the total number of trials.
In this case, we are given that the total number of trials is 520 and the number of successes is 200.
Therefore, the sample proportion is:
p̂ = (Number of successes) / (Total number of trials)
= 200 / 520
≈ 0.38
Rounding to two decimal places, the sample proportion is approximately 0.38.
To construct a test for a proportion, we use the sample test statistic called the proportion of successes, denoted by "p-hat". The formula to calculate p-hat is:
p-hat = x/n
Where:
- x is the number of successes in the sample
- n is the total number of trials (sample size)
In this case, you have been given that there are 520 trials and 200 successes. Plugging these values into the formula, we get:
p-hat = 200/520
Calculating this, we get:
p-hat = 0.3846
Rounding this value to two decimal places, the sample test statistic for this binomial experiment is approximately 0.38.