Question

Use this scenario for the following 2 questions A recent study asked university administrators if they worked most of their time remotely. The study found that 30% of them spend the majority of their time working remotely. Suppose a sample of 150 university administrators is taken. 2uestion 1 (1 point) ✓ Saved What is the probability that at least 51 of the administrators in the sample work remotely most of the time? 0.1525 0.1425 0.0544 0.0163 0.0644 ​ Question 2 (1 point) Which of the following statements is correct? Increasing the sample size to 600 increases the standard error by a factor of 2 . Changing the standard error doubles the magnitude of the standardized Z-value. Increasing the sample size to 600 increases the standard error by a factor of 2 . Changing the standard error decreases the standard Z-value to half of its original value Increasing the sample size to 600 decreases the standard error by a factor of 2 . Changing the standard error decreases the standard Z-value to half of its original value Increasing the sample size to 600 decreases the standard error by a factor of 2 . Changing the standard error doubles the magnitude of the standardized Z-value.

Answer 1

Question 1: The probability that at least 51 of the administrators in the sample work remotely most of the time is 0.0644.

Question 2: Increasing the sample size to 600 decreases the standard error by a factor of 2 and changes the standard error to decrease the standard Z-value to half of its original value.

Step-by-step explanation:

For Question 1, to find the probability that at least 51 administrators work remotely among the sample of 150, you can use the binomial probability formula. Calculate the cumulative probability of getting 51 or more administrators who work remotely. This probability turns out to be 0.0644.

Question 2 relates to the impact of changing sample size on the standard error and Z-value. Increasing the sample size to 600 decreases the standard error. As the sample size increases, the standard error reduces, indicating a better estimation of the population parameter. Moreover, decreasing the standard error affects the Z-value as well. The Z-value is obtained by dividing the difference between the sample mean and population mean by the standard error. When the standard error decreases, the Z-value decreases as well, making the estimation more reliable. Specifically, it reduces the magnitude of the Z-value to half of its original value, ensuring a more accurate representation of how many standard deviations the sample mean is from the population mean.