--%>
Assignment Help - homework help

Compute two sample standard deviations

Consider the following data for two independent random samples taken from two normal populations.

Sample 1 14 26 20 16 14 18

Sample 2 18 16 8 12 16 14

a) Compute the two sample means and the two sample standard deviations.

b) What is the point estimate of the difference between the two population means?

c) Assuming α = .10, conduct p-value based and critical-value based hypothesis tests for the equality

of means of the two populations.

d) What is the 90% confidence interval estimate of the difference between the two population means?

How do the results compare in all the three approaches to hypothesis testing?

 

E

Expert

Verified

Mean sample 1 = X1-bar = (14+26+20+16+14+18)/6 = 18

Mean sample 2 = X2-bar = (18+16+8+12+16+14)/6 = 14

Sample 1 SD = SD1

X1

X1-X1-bar

(X1-X1-bar)2

14

-4

16

26

8

64

20

2

4

16

-2

4

14

-4

16

18

0

0

Sum of (X1-X1-bar)2 = 104

S12 = 104/6-1

        = 20.8

SD1 =  = 4.56

Sample 2 SD = SD2

X2

X1-X1-bar

(X1-X1-bar)2

18

4

16

16

2

4

8

-6

36

12

-2

4

16

2

4

14

0

0

 

Sum of (X2-X2-bar)2 = 64

S22 = 64/6-1

        = 12.8

SD2 =  = 3.58

(b)

Point estimation of difference b/w two means = 18 - 14 = 4

(c)

t-test will be applied because sample size is small.

Hypothesis Formation

Null Hypothesis H0:    µ1 - µ2 = 0

Alternative Hypothesis H1:    µ1 - µ2 ≠ 0

t Statistic

t-statistic = (X1-bar  - x2-bar)/Sp

Where SP =

                  = 2.016

Critical value

Critical value of t with df=10 at 0.1 significance level = 1.812

Critical Region

Reject null hypothesis in favor of alternative if t is greater than t critical value of 1.812 or less than -1.812.

Computation

t-statistic = (18 - 14)/2.016

   = 5.95

Decision

Null hypothesis is rejected in favor of alternative as Z value is greater than Z critical value.

(d)

90% CI of difference between means = (18-14) - 1.812*2.016

                                                                    = 4 - 1.22 < µ < 4 + 1.22

                                                                    = 2.78< µ< 5.22

   Related Questions in Basic Statistics

  • Q : Cumulative Frequency and Relative

    Explain differences between Cumulative Frequency and Relative Frequency?

    		•
  • Q : MANOVA and Reflection Activity

    Activity 10:   MANOVA and Reflection   4Comparison of Multiple Outcome Variables This activity introduces you to a very common technique - MANOVA. MANOVA is simply an extension of an ANOV

    		•
  • Q : What is Inter-arrival times

    Inter-arrival times:A) Requests arrive randomly, often separated by small time intervals with few long separations among themB) The time until the next arrival is independent of when the last arrival occurredC) Coro

    		•
  • Q : Assumptions in Queuing system

    Assumptions in Queuing system: • Flow balance implies that the number of arrivals in an observation period is equal to the

    		•
  • Q : Calculate the p- value Medical tests

    Medical tests were conducted to learn about drug-resistant tuberculosis. Of 284 cases tested in New Jersey, 18 were found to be drug- resistant. Of 536 cases tested in Texas, 10 were found to be drugresistant. Do these data indicate that New Jersey has a statisti

    		•
  • Q : Hypothesis homework A sample of 9 days

    A sample of 9 days over the past six months showed that a clinic treated the following numbers of patients: 24, 26, 21, 17, 16, 23, 27, 18, and 25. If the number of patients seen per day is normally distributed, would an analysis of these sample data provide evidence that the variance in the numbe

    		•
  • Q : Sample Questions in Graphical Solution

    Solved problems in Graphical Solution Procedure, sample assignments and homework Questions: Minimize Z = 10x1 + 4x2 Subject to

  • Q : Principles of data analysis For the

    For the data analysis project, you will address some questions that interest you with the statistical methodology we are learning in class. You choose the questions; you decide how to collect data; you do the analyses. The questions can address almost any topic,

    		•
  • Q : Compare the test results The grade

    The grade point averages of 61 students who completed a college course in financial accounting have a standard deviation of .790. The grade point averages of 17 students who dropped out of the same course have a standard deviation of .940. Do the data indicate a

    		•
  • Q : State Littles Law Little’s Law : • L =

    Little’s Law: • L = λR = XR • Lq = λW = XW • Steady state system • Little’s Law holds as long as customers are not destroyed or&nbs

    		•