An athletics coach claims that the amount of illegal substances in his supplemen
ID: 1095136 • Letter: A
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