--%>
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 : Spss in Business and Management Please

    Please tell me the cost of this current assignment. Note : I do not want the Solutions but please tell me the price as the assignment is .. Is the cost 3 euro? Do you sell those questions?

    		•
  • Q : Sample Questions in Graphical Solution

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

  • 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

    		•
  • Q : Problems on ANOVA We are going to

    We are going to simulate an experiment where we are trying to see whether any of the four automated systems (labeled A, B, C, and D) that we use to produce our root beer result in a different specific gravity than any of the other systems. For this example, we would l

    		•
  • Q : STATISTICS Question This week you will

    This week you will analyze if women drink more sodas than men.  For the purposes of this Question, assume that in the past there has been no difference.  However, you have seen lots of women drinking sodas the past few months.  You will perform a hypothesis test to determine if women now drink more

    		•
  • 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 : Compute the stoke statistics Please do

    Please do the following and submit your results in the table format in a word file on canvas: a)      Go to Yahoo finance/Investing/Stocks/Research tools/Historical quotes/Historical prices and download adjusted monthly closing prices for the period 1/1/2006 to 31

    		•
  • Q : Homework help on Human memory & SPSS

    Effect of Scopolamine on Human Memory: A Completely Randomized Three Treamtent Design (N = 28) Scopolamine is a sedative used to induce sle

    		•
  • 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 : 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

    		•