Question

A hypothesis testing:

H0: p=0.57
HA: p>0.57
We conduct a survey with sample size n=835 and have P=0.77. Find the test statistic z associated with the sample proportion. Note: decimal places.

Answer 1

To find the test statistic z associated with the sample proportion, calculate the standard error of the proportion using the formula SE = sqrt((p * (1 - p))/n). Then, calculate the z-score using the formula z = (p - P0) / SE, where P0 is the hypothesized population proportion.

Step-by-step explanation:

To find the test statistic z associated with the sample proportion, we first need to calculate the standard error of the proportion. The formula for the standard error of the proportion is SE = sqrt((p * (1 - p))/n), where p is the sample proportion and n is the sample size. In this case, p = 0.77 and n = 835.

SE = sqrt((0.77 * (1 - 0.77))/835) = 0.0139

Next, we calculate the z-score using the formula z = (p - P0) / SE, where P0 is the hypothesized population proportion. In this case, P0 = 0.57.

z = (0.77 - 0.57) / 0.0139 = 14.39 (rounded to two decimal places)