Question

Q1. In order to estimate the average time spent on the computer terminals per student at a local university, data were collected from a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.2 hours. If the sample mean is 9 hours, then the 95% confidence interval is approximately

	a.	7.04 to 10.96 hours
	b.	7.36 to 10.64 hours
	c.	8.74 to 9.26 hours
	d.	7.80 to 10.20 hours

Q2. In a random sample of 500 college students, 23% say that they read or watch the news every day. Develop a 90% confidence interval for the population proportion.

	a.	0.199 to 0.261
	b.	0.206 to 0.254
	c.	0.193 to 0.267
	d.	0.215 to 0.245

Q3. A random sample with n=54 provided sample mean of 22.5 and a sample standard deviation of 4.4, develop a 99% confidence interval for the population mean.

	a.	20.96 to 24.04
	b.	20.90 to 24.10
	c.	19.90 to 24.20
	d.	None of the above

Q4. Find t- value that upper tail area is 0.025 with 12 degrees of freedom

Thanks!

Answer 1

1)
sample mean, xbar = 9
sample standard deviation, σ = 1.2
sample size, n = 81

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

ME = zc * σ/sqrt(n)
ME = 1.96 * 1.2/sqrt(81)
ME = 0.26

CI = (xbar - Zc * s/sqrt(n) , xbar + Zc * s/sqrt(n))
CI = (9 - 1.96 * 1.2/sqrt(81) , 9 + 1.96 * 1.2/sqrt(81))
CI = (8.74 , 9.26)

2)

sample proportion, = 0.23
sample size, n = 500
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.23 * (1 - 0.23)/500) = 0.019

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, Zc = Z(α/2) = 1.64

Margin of Error, ME = zc * SE
ME = 1.64 * 0.019
ME = 0.031

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.23 - 1.64 * 0.019 , 0.23 + 1.64 * 0.019)
CI = (0.199 , 0.261)

3)

sample mean, xbar = 22.5
sample standard deviation, s = 4.4
sample size, n = 54
degrees of freedom, df = n - 1 = 53

Given CI level is 99%, hence α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005, tc = t(α/2, df) = 2.672

ME = tc * s/sqrt(n)
ME = 2.672 * 4.4/sqrt(54)
ME = 1.6

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (22.5 - 2.672 * 4.4/sqrt(54) , 22.5 + 2.672 * 4.4/sqrt(54))
CI = (20.90 , 24.10)

4)
for α = 0.025 and df = 12
t value is 2.179.