Question

Claim: Most adults would erase all of their personal information online if they could. A software firm survey of 433 randomly selected adults showed that 59​% of them would erase all of their personal information online if they could. Find the value of the test statistic.

Answer 1

To find the value of the test statistic, calculate the standard error of the sample proportion and then calculate the test statistic using the difference between the sample proportion and the claimed proportion.Therefore, the value of the test statistic is approximately 0.344.

Step-by-step explanation:

To find the value of the test statistic, we first need to calculate the standard error of the sample proportion. The formula for the standard error is:

SE = sqrt((p * (1 - p)) / n)

Where p is the sample proportion (in this case, 0.59) and n is the sample size (433).

Plugging in the values, we get:

SE = sqrt((0.59 * (1 - 0.59)) / 433)

SE = sqrt(0.24 / 433)

SE = sqrt(0.000554)

SE ≈ 0.02358

Now we can calculate the test statistic, which is the difference between the sample proportion and the claimed proportion divided by the standard error:

Test statistic = (0.59 - 0.5) / 0.02358

Test statistic ≈ 0.344

Therefore, the value of the test statistic is approximately 0.344.