Question

11.

Give a 95% confidence interval, for μ1−μ2μ1-μ2 given the following information.

n1=25n1=25, ¯x1=2.65x¯1=2.65, s1=0.91s1=0.91
n2=45n2=45, ¯x2=2.45x¯2=2.45, s2=0.83

---------- ± -----------  Use Technology Rounded to 2 decimal places.

13.

Two samples are taken with the following numbers of successes and sample sizes
r1r1 = 36 r2r2 = 33
n1n1 = 60 n2n2 = 100

Find a 99% confidence interval, round answers to the nearest thousandth.
---------- < p1−p2p1-p2 < ------------

14.

Two samples are taken with the following sample means, sizes, and standard deviations
¯x1x¯1 = 40 ¯x2x¯2 = 27
n1n1 = 50 n2n2 = 45
s1s1 = 5 s2s2 = 3

Estimate the difference in population means using a 94% confidence level. Use a calculator, and do NOT pool the sample variances. Round answers to the nearest hundredth.
---------- < μ1−μ2μ1-μ2 < ------------

16.

You wish to test the following claim (HaHa) at a significance level of α=0.02α=0.02.

      Ho:p1=p2Ho:p1=p2
      Ha:p1>p2Ha:p1>p2

You obtain 29.1% successes in a sample of size n1=508n1=508 from the first population. You obtain 24.6% successes in a sample of size n2=783n2=783 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

Answer 1

11)

Two-Sample T-Test and CI

Method

μ₁: mean of Sample 1

µ₂: mean of Sample 2

Difference: μ₁ - µ₂

Equal variances are assumed for this analysis.

Descriptive Statistics

Sample	N	Mean	StDev	SE Mean
Sample 1	25	2.650	0.910	0.18
Sample 2	45	2.450	0.830	0.12

Estimation for Difference

Difference	Pooled StDev	95% CI for Difference
0.200	0.859	(-0.23, 0.63)

13)

Test and CI for Two Proportions

Method

p₁: proportion where Sample 1 = Event

p₂: proportion where Sample 2 = Event

Difference: p₁ - p₂

Descriptive Statistics

Sample	N	Event	Sample p
Sample 1	60	36	0.600000
Sample 2	100	33	0.330000

Estimation for Difference

Difference	99% CI for Difference
0.27	(0.07, 0.47)

CI based on normal approximation

14)

Equal variances are not assumed for this analysis.

Descriptive Statistics

Sample	N	Mean	StDev	SE Mean
Sample 1	50	40.00	5.00	0.71
Sample 2	45	27.00	3.00	0.45

Estimation for Difference

Difference	94% CI for Difference
13.000	(11.40, 14.60)

16)

given p1 = 0.291, n1 = 508

p2 = 0.246, n2 = 783

test statistic z =

= 0.264

by substituting all the values in the equation

The value of test statistic z is 1.793

p-value = 0 .03673