Question

The International Tennis Federation (ITF) requires that tennis balls have an average diameter of 6.7 centimetres. Tennis balls being produced by one manufacturer are tested to see if they fail to meet the ITF standard. A random sample of 10 tennis balls had a mean diameter of 6.85 cm, with standard deviation 0.32 cm. Assume tennis ball diameter is normally distributed.
Enter your responses to all parts in the text box below.  

a) Choose the correct hypotheses to test the research hypothesis that the manufacturer's tennis balls fail to meet the ITF standard. (1 mark)
Write only the letter corresponding to the answer.

b) Perform the hypothesis test. (4 marks)
i.e. Calculate then state the test statistic value, the P-value and your conclusion in the context of the question. Use α = 0.10.

c) Calculate then give a 90% confidence interval for the true mean diameter and interpret your interval.   (3 marks)

d) Comment on the hypothesis test conclusion from part b) in relation to the confidence interval found in part c). (2 marks)

A. Ho: Md = 0 Ha: Md > 0 B. Ho: Mi = M2 Ha: H1 > M2 C. Ho: M1 = 6.85 Hai u + 6.85 D. Ho: y = = 6.7 Ha: y + 6. 85 E. Ho: = = 6.7 Hail = 6.7

Answer 1

Given l= 6.7 cm s = 0,32cm n=10 X= 6-85 com a Hypothesis Hol lle 6.7 Hail & 6.7 option © is cospect. b) Test statistic t = X-1 SNO = 6-85- 6-7 0.32/V10 14823 P-value = 0.1724 Here p-value = 0.1724 > a=0.10 - Accept the null Hypothesis Conclusion: The ITE Tennis ball have an average diameter of 6.7 cm. O gol confidence interval * I to 12 ( 5 ) 6.85 € 1,8331/ 0.32 8331(033) 6.85 1 0.1855 CI [6.6645 7.0355] we can say, got. confident that the population mean (True between 6.6645 and 7:0355 9 mean diam) falls 1 an d from part 6 we conclude that TIE tennis ball have average diameter 6.7 em and from © we conclude that this diameter lies between got confidence internal. ie got confident that true mean diameter of The tennis between [6.6645 , 7.0355) ball is