(c) Suppose that a random sample of size n is drawn from a population with mean µ = 220 and standard deviation σ
i. Determine the required sample size such that the standard error of the sample mean is reduced to less than 3.
ii. Determine the required sample size if we want to be 90% confident that the maximum error is 5.
(a) A video game company is studying teenagers' time spent playing video games weekly, in Hong Kong and Taiwan. Assume that the time spent playing video games by teenagers in Hong Kong and Taiwan has a normal distribution for both populations of teenagers and that the standard deviations for the two populations are equal. A sample of 13 teenagers from Hong Kong showed that the mean time they spend playing video games is 24 hours per week with a standard deviation of 2 hours. Another sample of 14 teenagers from Taiwan showed that the mean time spent by them playing video games is 21 hours per week with a standard deviation of 3 hours. Using a 1% significance level, can you conclude that the mean time spent playing video games by teenagers in Hong Kong is higher than that for teenagers in Taiwan?
(b) The number of emails arriving at a server per minute is claimed to follow a Poisson distribution. To test this claim, the number of emails arriving in 70 randomly chosen 1-minute intervals is recorded. The table below summarizes the result.
Number of emails 0 1 2 ≥ 3
Observed Frequency 13 22 23 12
Test the hypothesis that the number of emails per minute follows a Poisson distribution? Use a significance level of α = 0.05.
(c) In a volunteer group, adults 21 and older volunteer from one to nine hours each week to spend time with a disabled senior citizen. The program recruits among community college students, four-year college students, and nonstudents. The table below is a sample of the adult volunteers and the number of hours they volunteer per week.
Type of Volunteer 1-3 Hours 4-6 Hours 7-9 Hours
Community College Students 111 96 48
Four-Year College Students 96 133 61
Nonstudents 91 150 53
At α = 0.05 confidence level, is there enough evidence to conclude that the number of hours volunteered is independent of the type of volunteer?
These problems can be solved by conduct a hypothesis: t-test right-tail; chi-square test for goodness... View the full answer