An athletics coach claims that the amount of illegal substances in his supplemen

Question

An athletics coach claims that the amount of illegal substances in his supplements should be normally distributed with a mean of 10 milligrams and standard deviation of 2 milligrams. Obviously for the purposes of avoiding detection and also maximisation of performance, his country's olympic committee would like to know if this is true. Use a 5% level of significance. They have taken a random sample of 8 tablets and tested them: Tablet Illegal Substance(mg)

1 6.2

2 7.1

3 10.7

4 10.8

5 10.8

6 10.9

7 11.2

8 11.7

1. What is the value of the F(x) for the first tablet? (4 decimal places)Blank 1

2. What is the value of the test statistic, D? (4 decimal places)Blank 2

3. Is the null hypothesis rejected? (enter yes or no)Blank 3

4. On the basis of this test, is the amount of illegal substances in the coach's supplements normally distributed with a mean of 10 milligrams and standard deviation of 2 milligrams.(enter yes or no) Blank 4

Explanation / Answer

CALCULATIONS: Sample Mean=(6.2+7.1+10.7+10.8+10.8+10.9+11.2+11.7)/8 9.93 Variance=(9.925-6.2)^2+(9.925-7.1)^2+(9.925-10.7)^2+2*(9.925-10.8)^2+(9.925-10.9)^2+(9.925-11.2)^2+(9.925-11.7)^2 29.72 Standard Deviation = Square Root (29.715/7) 2.06 Standard Error = S.D/square root of n,n is the sample size 0.73 At 5% level of significance , z value =1.96 Population Parameter will be 9.93+/-0.73 9.20 10.66 ANSWERS: 2.The value of the test statistics : Mean: 9.93 and S.D.: 0.73 3.No the null hypothesis is accepted as the range was 8-12 miligram(10+/-2) 4.Yes the illegal substances in the coach's supplements normally distributed with a mean of 10 milligrams and standard deviation of 2 milligrams

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