# Question

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?

(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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