--%>
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 : Random variables Random variables with

    Random variables with zero correlation are not necessarily independent. Give a simple example.    

    		•
  • Q : Probability of winning game Monte Carlo

    Monte Carlo Simulation for Determining Probabilities 1. Determining the probability of winning at the game of craps is difficult to solve analytically. We will assume you are playing the `Pass Line.'  So here is how the game is played: The shooter rolls a pair of

    		•
  • Q : Frequency Distributions Define the term

    Define the term Frequency Distributions?

    		•
  • Q : Probability problem A) What is the

    A) What is the probability of getting the following sequence with a fair die (as in dice):B) What is the probability of getting the same sequence with a die that is biased in the following way: p(1)=p(2)=p(3)=p(4)=15%;

    		•
  • Q : Describe how random sampling serves

    Explain sampling bias and describe how random sampling serves to avoid bias in the process of data collection.    

    		•
  • Q : Analyse the statistics of the data

    Assigment Question Select any two manufacturing companies and formulate the cost and revenue functions of the companies. analyse the statistics of the data and then sketch the functions and determine their breakeven points. (Note: You are required to interview the production and sales manag

    		•
  • Q : Describe what happens to the confidence

     A nurse practitioner working in a dermatology clinic is studying the efficacy of tretinoin in treating women's post partum abdominal stretch marks.  From a sample of 15 women, the mean reduction of stretch mark score is -0.33 with a sample standard deviation of 2.46.  Describe wha

    		•
  • 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 : 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 : Problem related to playing cards Cards

    Cards are randomly drawn one at the time and with replacement from a standard deck of 52 playing cards. (a) Find the probability of getting the fourth spades on the 10th draw. (b) Determine the

    		•