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.

Exercise vigorous enough to increase heart rate to between 50% and 85% of maximum heart rate is recommended for good health. Does boxing high intensity interval training (HIIT) or cardio tennis increase heart rate the most? Ten subjects participated in two different 45 minute exercise classes - boxing HIIT and cardio tennis. At the end of each class their heart rate (beats per minute) was recorded.

Subject 1 2 3 4 5 6 7 8 9 10 Boxing HIIT 145 168 157 129 189 135 165 172 127 148 Cardio 152 159 tennis 143 122 162 130 154 175 132 146 a) Should the results best be analysed as paired data or two independent means? Explain. b) Briefly describe how this experiment could be designed to help avoid biased results. c) Is there a significant difference in heart rate between boxing HIIT and cardio tennis? Carry out a hypothesis test using a = 0.05, showing all steps. d) Calculate a 95% confidence interval for the difference in heart rate between the two classes and interpret your interval in context. Based on your hypothesis test result, did you expect to find 0 in the interval? Explain