--%>
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 : Networks of queues Networks of queues •

    Networks of queues • Typically, the flow of customers/request through a system may involve a number of different processing nodes.– IP packets through a computer network– Orders through a manufactur

    		•
  • Q : Point of estimate standing data se to

    standing data se to develop a point of estimate

    		•
  • Q : What is your conclusion The following

    The following data were collected on the number of emergency ambulance calls for an urban county and a rural county in Florida. Is County type independent of the day of the week in receiving the emergency ambulance calls? Use α = 0.005. What is your conclusion? Day of the Week<

    		•
  • Q : Write out the null hypothesis 1.

    1. (AAC/ACA c9q1).  For each of the following studies, decide whether you can reject the null hypothesis that the groups come from identical populations. Use the alpha = .05 level.1a.

  • Q : What is Interactive Response Time Law

    Interactive Response Time Law: • R = (L/X) - Z• Applies to closed systems.• Z is the think time. The time elapsed since&nb

    		•
  • Q : Correlation analysis and the regression

    1).  When you take out a mortgage, there are many different kinds of costs.  Usually the two largest are the interest rate (annual percentage that determines the size of your monthly payment) and the loan fee (a one-time percentage charged to you at the time

    		•
  • Q : Building Models Building Models • What

    Building Models • What do we need to know to build a model?– For model checking we need to specify behavior • Consider a simple vending machine – A custome rinserts coins, selects a beverage and receives a can of soda &bul

    		•
  • Q : Model Checking Approach Model Checking

    Model Checking Approach: • Specify program model and exhaustively evaluate that model against a speci?cation        –Check that properties hold   

  • Q : 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) Com

    		•
  • Q : Simplified demonstration of Littles Law

    Simplified demonstration of Little’s Law:

    Discover Q & A

    Leading Solution Library
    Avail More Than 1456758 Solved problems, classrooms assignments, textbook's solutions, for quick Downloads
    No hassle, Instant Access
    Start Discovering

    18,76,764

    1931490
    Asked

    3,689

    Active Tutors

    1456758

    Questions
    Answered

    Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!

    Submit Assignment
    Home | Company Overview | Services | Discover Q&A | Sitemap | Contact Us | T & C | Refund Policy | Copyright Policy | Blog | Q&A | Directory

    ©TutorsGlobe All rights reserved 2022-2023.