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.

Match Lengths (minutes)Wimbledon Match Lengths
(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 84 231 122115 87 137 101 119 138 132 136 111 194 92 198 153 256 146 149 103 116 163 182 132 123 178 140 151 115 107 202 128 60 89 94 95 89 182 Wimbledon Match Lengths 60 80 100 120 140 160 180 200 220 240 260 Match Lengths (minutes)