--%>
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 : Explain Queuing theory Queuing theory :

    Queuing theory: • Queuing theory deals with the analysis of lines where customers wait to receive a service:

    Q : Use the NW corner rule to find an

      (a) Use the NW corner rule to find an initial BFS, then solve using the transportation simplex method. Indicate your optimal objective function value. (b) Suppose we increase s1 from 15 to 16, and d3 from 10 to 11. S

    		•
  • Q : Variance and standard error A hospital

    A hospital treated 412 skin cancer patients over a year. Of these, 197 were female. Give the point estimate of the proportion of females seeking treatment for skin cancer. Give estimates of the

    		•
  • 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 : Data Description 1. If the mean number

    1. If the mean number of hours of television watched by teenagers per week is 12 with a standard deviation of 2 hours, what proportion of teenagers watch 16 to 18 hours of TV a week? (Assume a normal distribution.) A. 2.1% B. 4.5% C. 0.3% D. 4.2% 2. The probability of an offender having a s

    		•
  • 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 : Program Evaluation and Review

    Program Evaluation and Review Technique (PERT) A) Developed by US Navy and a consulting firm in 1958 for the Polaris submarine project. B) Technique as for CPM method, but acti

    		•
  • Q : Report on Simple Random Sampling with

    One of my friend has a problem on simple random sampling. Can someone provide a complete Report on Simple Random Sampling with or without replacement?

    		•
  • 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 : Explain Service times Service times: A)

    Service times:A) In most cases, servicing a request takes a “short” time, but in a few occasions requests take much longer.B) The probability of completing a service request by time t, is independent of how much tim

    		•