--%>
Assignment Help - homework help

conclusion using p-value and critical value approaches

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 number of patients seen per day is less than 10? Use α = .025 level of significance. What is your conclusion using p-value and critical value approaches. Is the conclusion different in both the cases?

E

Expert

Verified

 

Hypothesis Formation

H0: σ =10

H1: σ < 10

Test Statistics

χ2 = (n-1).S2/ σ2

Critical Region

Reject H0 in favor of alternative if χ2 test statistic lesser than the critical value of χ2

i.e χ2test statistic < critical χ2

Critical value of χ2 at 0.025 Significance Level for single tail test

Df = n – 1 = 9 – 1 = 8

Critical value of χ2 with df 8 and alpha 0.025 = 2.18

Computation

Data (X)

X – X-bar

(X-X-bar)2

24

2.111111

4.45679

26

4.111111

16.90123

21

-0.88889

0.790123

17

-4.88889

23.90123

16

-5.88889

34.67901

23

1.111111

1.234568

27

5.111111

26.12346

18

-3.88889

15.12346

25

3.111111

9.679012

 

Sum of (X-X-bar)2 = 132.89

S2 = 132.89/9-1

     = 16.61 

χ2 = (9-1)*16.61/10

    = 13.29

Decision

As χ2 statistic is not less than critical value, therefore we can’t say that variance is less than 10. P-value for critical value is 0.01 and it is approximately found from χ2 table.  P-value is greater than our tolerance for ambiguity therefore we can’t that variance is significantly lower than 10.

 

   Related Questions in Advanced Statistics

  • Q : Correlation Define the term Correlation

    Define the term Correlation and describe Correlation formula in brief.

    		•
  • Q : Frequency Distributions Define the term

    Define the term Frequency Distributions?

    		•
  • Q : Problem on Chebyshevs theorem 1. Prove

    1. Prove that the law of iterated expectations for continuous random variables.2. Prove that the bounds in Chebyshev's theorem cannot be improved upon. I.e., provide a distribution which satisfies the bounds exactly for k ≥1, show that it satisfies the

    		•
  • Q : Find the cumulative distribution

    You must use the pre-formatted cover sheet when you hand in the assignment. Out full detailed solutions. Sloppy work will naturally receive a lower score. 1. Suppose at each step, a particle moving on sites labelled by integer has three choices: move one site to the right with pro

    		•
  • Q : Variation what are the advantages and

    what are the advantages and disadvantages of seasonal variation

    		•
  • Q : What is your statistical decision

    Question 1 Do parents with more children travel more than parents of small families? To find out, a survey was done of a large number of adults. Respondents were asked how many children they had and how many times

    		•
  • Q : Bayesian Point Estimation What are the

    What are the Bayesian Point of estimation and what are the process of inference in Bayesian statistics?

    		•
  • Q : MANOVA and Reflection Activity 10:

    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 ANOVA and allows for the comparison of multiple outcome variables (again, a very common situation in research a

    		•
  • Q : Null hypothesis In testing the null

    In testing the null hypothesis H0: P=0.6 vs the alternative H1 : P < 0.6 for a binomial model b(n,p), the rejection region of a test has the structure X ≤ c, where X is the number of successes in n trials. For each of the following tests, d

    		•
  • Q : Problem on Poisson distribution The

    The number of trucks coming to a certain warehouse each day follows the Poisson distribution with λ= 8. The warehouse can handle a maximum of 12 trucks a day. What is the probability that on a given day one or more trucks have to be sent away? Round the answer

    		•