Question

A survey of 813 adult inhabitants of the town of Tuckborough reveals that 0.59 of them (that is, 59% ) are farmers. ou set up a hypothesis test to check whether it is reasonable to conclude that more than 0.592 (that is, more than 59.2% ) of the adult inhabitants are farmers. You choose a level of ignificance α=0.05. Compute the value of the appropriate test statistic, rounded to 2 decimal places:

Answer 1

To compute the appropriate test statistic, calculate the standard error of the proportion using the formula SE = sqrt((p * (1 - p)) / n). Then, calculate the test statistic by subtracting the hypothesized proportion from the sample proportion and dividing by the standard error.

Step-by-step explanation:

To compute the appropriate test statistic, we first need to calculate the standard error of the proportion. The formula for the standard error of a proportion is: SE = sqrt((p * (1 - p)) / n), where p is the sample proportion and n is the sample size. In this case, p = 0.59 and n = 813, so we have: SE = sqrt((0.59 * (1 - 0.59)) / 813). Calculating this gives us a standard error of approximately 0.014.

Next, we can calculate the test statistic by subtracting the hypothesized proportion from the sample proportion and dividing by the standard error: test statistic = (sample proportion - hypothesized proportion) / standard error. In this case, the hypothesized proportion is 0.592, so we have: test statistic = (0.59 - 0.592) / 0.014. After calculating this, we get a test statistic of approximately -0.14.