Question

A study examined possible reasons for students going on academic probation. Students who spent more than 20 hours a week playing video games were classified as "heavy gamers." Of the 342 students on academic probation in the study, 127 were found to be heavy gamers.

Calculate the point estimate of the proportion of students on academic probation that are heavy gamers. Round to 2 decimal places.

Calculate the 95% confidence interval for the proportion of students that are on academic probation that are heavy gamers. Input the lower bound. Round to 2 decimal places.

Calculate the 95% confidence interval for the proportion of students that are on academic probation that are heavy gamers. Input the upper bound. Round to 2 decimal places.

Student Services believes the proportion of students on academic probation that are heavy gamers has decreased from 45% in 2015. Test the claim using =0.05. Round to 3 decimal places.

Answer 1

sample proportion, = 0.3713
sample size, n = 342
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.3713 * (1 - 0.3713)/342) = 0.0261

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

Margin of Error, ME = zc * SE
ME = 1.96 * 0.0261
ME = 0.0512

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.3713 - 1.96 * 0.0261 , 0.3713 + 1.96 * 0.0261)
CI = (0.32 , 0.42)

Lower bound = 0.32
Upper bound = 0.42

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.45
Alternative Hypothesis, Ha: p < 0.45

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.3713 - 0.45)/sqrt(0.45*(1-0.45)/342)
z = -2.926

P-value Approach
P-value = 0.0017 (p value = 0.002 upto 3 decimal)
As P-value < 0.05, reject the null hypothesis.