A tennis enthusiast wants to estimate the mean length of men’s singles matches held during the Wimbledon tennis tournament. From the Wimbledon history archives, he randomly selects 40 matches played during the tournament since the year 1968 (when professional players were first allowed to participate). The lengths of the 40 selected matches, in minutes, follow:

(a) Obtain a point estimate of the population mean length of men’s singles matches during Wimbledon.

(b) A frequency histogram of the data is shown next. Explain why a large sample is necessary to construct a confidence interval for the population mean length of men’s singles matches during Wimbledon.

(c) Construct and interpret a 90% confidence interval for the population mean length of men’s singles matches during Wimbledon.

(d) Construct and interpret a 95% confidence interval for the population mean length of men’s singles matches during Wimbledon.

(e) What effect does increasing the level of confidence have on the interval?

(f) Do the confidence intervals computed in parts (c) and (d) represent an estimate for the population mean length of men’s singles matches during all professional tennis tournaments? Why?

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110 76 231 84 137 122 115 87 136 149 101 119 132 194 111 92 138 146 256 153 198 103 163 116 151 115 182 132 140 107 178 123 89 202 60 182 128 89 94 95 Wimbledon Match Lengths 9. 60 80 100 120 140 160 180 200 220 240 260 Match Lengths (minutes) 6, 4) 2. Frequency