--%>
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 : Define Service Demand Law

    Service Demand Law:• Dk = SKVK, Average time spent by a typical request obtaining service from resource k• DK = (ρk/X

    		•
  • Q : Problem on Model Checking Part (a).

    Part (a). Draw a state diagram for a car with the following state variables: D indicating whether the car is in drive; B indicating the brake pedal is depressed; G indicating the gas pedal is depressed; and M indicating whether the car is moving. (For example, the sta

    		•
  • 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 : Probability how can i calculate

    how can i calculate cumulative probabilities of survival

    		•
  • 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 : Cumulative Frequency and Relative

    Explain differences between Cumulative Frequency and Relative Frequency?

    		•
  • Q : Computing Average revenue using

    Can anyone help me in the illustrated problem? The airport branch of a car rental company maintains a fleet of 50 SUVs. The inter-arrival time between the requests for an SUV is 2.4 hrs, on an average, with a standard deviation of 2.4 hrs. There is no indication of a

    		•
  • 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 : Safety and Liveness in Model Checking

    Safety and Liveness in Model Checking Approach; •? Safety: Nothing bad happens •? Liveness: Something good happens •? Model checking is especially good at verifying safety and liveness properties    –?Concurrency i

    		•
  • Q : Statics for each of the following

    for each of the following studies a and b decide whether to reject the null hypothesis that groiups come from identical populations. Use the .01 level. (c) Figure the effects size for each study. (d) ADVANCED TOPIC: Carry out an analysis of variance for study (a) using the strucurtal method.

    		•