The International Tennis Federation (ITF) requires that tennis balls have an average diameter of 6.70 centimetres. Tennis balls being produced by one manufacturer are tested to see if they meet the ITF standard. A random sample of 15 tennis balls is taken and the diameters (in cm) are shown below.

6.74 6.64 6.71 6.57 6.91 6.65 6.80 6.72 6.50 6.62 6.54 6.85 6.73 6.79 6.67

a)Create a 98% confidence interval for the mean diameter of tennis balls produced by the manufacturer and interpret your interval in context.

b)Perform a hypothesis test to see if there is evidence that the manufacturer's tennis balls are smaller than the ITF standard. Use=0.01.

c)Explain how your confidence interval and hypothesis test conclusion support each other.

d)Are the assumptions required for the test you performed met? Discuss briefly.