Question

9. For the next three questions, use the following information to determine your answers: A survey was sent out to re-evalute the proportion of people who play games on pc computers, as the last study on the topic had been gathered four years prior. The current study, with 861 participants, found that 53% of people who responded play on a pc computer.

Calculate the 90% confidence interval. Enter your answer in the following format: (lower_value, upper_value). Please round your values to the fourth decimal point.

10. This survey was done to test the possibility that fewer people are playing games on pc computers. The previous study found that 81% of people were playing games on pc computers. Which of the following represents the hypotheses that we will be testing, assuming that p represents the most recent findings and that p0 represents the older findings in the previous study.

Choose:

H0: p0 ≥ 0.81 versus Ha: p0 < 0.81

H0: p ≥ 0.81 versus Ha: p < 0.81

H0: p0 = 0.81 versus Ha: p0 ≠ 0.81

H0: p ≤ 0.81 versus Ha: p > 0.81

11. Calculate the p-value and determine if we should accept or reject H0 under alpha = 0.05.

Answer 1

9) The 90% confidence interval is

+/- z_0.05 * sqrt((1 - )/n)

= 0.53 +/- 1.645 * sqrt(0.53 * (1 - 0.53)/861)

= 0.53 +/- 0.0280

= 0.5020, 0.5580

10) H0: P > 0.81

H1: P < 0.81

11) The test statistic z = ( - P)/sqrt(P(1 - P)/n)

= (0.53 - 0.81)/sqrt(0.81 * (1 - 0.81)/861)

= -20.94

P-value = P(Z < -20.94)

= 0.0000

Since the p-value is less than alpha = 0.05, so we should reject H0.