--%>
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 : Pearsons correlation coefficient The

    The table below illustrates the relationship between two variable X and Y. A

    		•
  • Q : Problem on income probability Kramer

    Kramer spends all of his income  $270  on two products, soup (S) and on golf balls (G). He always bought 2 golf balls for every 1 cup of soup he consumes. He acquires no additional utility from the other cup of soup unless he as well gets 2 more golf balls a

    		•
  • Q : Problem on layout A manufacturing

    A manufacturing facility consists of five departments, 1, 2, 3, 4, and 5. It produces four components having manufacturing product routings and production volumes indicated below.   1. Generate the from-to matrix and the interaction matrix. Use a

    		•
  • 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 : Analysing the Probabilities 1. In the

    1. In the waning seconds of Superbowl XLVII, the Baltimore Ravens elected to take a safety rather than punt the ball. A sports statistician wishes to analyze the effect this decision had on the probability of winning the game. (a) Which two of the following probabilities would most help t

    		•
  • 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 : 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 : Probability Distributions and Data

    1. A popular resort hotel has 300 rooms and is usually fully booked. About 4% of the time a reservation is canceled before 6:00 p.m. deadline with no penalty. What is the probability that at least 280 rooms will be occupied? Use binomial distribution to find the exact value and the normal approxi

    		•
  • Q : True and False Statement Discuss the

    Discuss the following statements and explain why they are true or false: a)      Increasing the number of predictor variables will never decrease the R2 b)      Multicollinearity affects the int

    		•
  • Q : Calculate confidence interval A nurse

    A nurse anesthetist was experimenting with the use of nitronox as an anesthetic in the treatment of children's fractures of the arm.  She treated 50 children and found that the mean treatment time (in minutes) was 26.26 minutes with a sample standard deviation of

    		•