--%>
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 : Calculate corresponding t value or s

    1)    Construct a 99% confidence interval for the population mean µ.   2)    At what significance level do the data provide good evidence that the average body temperature is

    		•
  • Q : Random variables Random variables with

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

    		•
  • 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 : Frequency Distributions Define the term

    Define the term Frequency Distributions?

    		•
  • 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 : Variation what are the advantages and

    what are the advantages and disadvantages of seasonal variation

    		•
  • 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 : 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 : How you would use randomization in

    The design of instrument controls affects how easily people can use them. An investigator used 25 students who were right-handed to determine whether right-handed subjects preferred right-handed threaded knobs. He had two machines that differed only in that one had a

    		•
  • 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

    		•