# Question

The following data represent the ages of the winners of the Academy Award for Best Actor for the years 2004–2009.

004: Jamie Foxx ........... 37

2005: Philip Seymour Hoffman ..... 38

2006: Forest Whitaker ........ 45

2007: Daniel Day-Lewis ........ 50

2008: Sean Penn ........... 48

2009: Jeff Bridges ......... 60

(a) Compute the population mean, µ.

(b) List all possible samples with size n = 2. There should be 6C2 = 15 samples.

(c) Construct a sampling distribution for the mean by listing the sample means and their corresponding probabilities.

(d) Compute the mean of the sampling distribution.

(e) Compute the probability that the sample mean is within 3 years of the population mean age.

(f ) Repeat parts (b)–(e) using samples of size n = 3. Comment on the effect of increasing the sample size.

004: Jamie Foxx ........... 37

2005: Philip Seymour Hoffman ..... 38

2006: Forest Whitaker ........ 45

2007: Daniel Day-Lewis ........ 50

2008: Sean Penn ........... 48

2009: Jeff Bridges ......... 60

(a) Compute the population mean, µ.

(b) List all possible samples with size n = 2. There should be 6C2 = 15 samples.

(c) Construct a sampling distribution for the mean by listing the sample means and their corresponding probabilities.

(d) Compute the mean of the sampling distribution.

(e) Compute the probability that the sample mean is within 3 years of the population mean age.

(f ) Repeat parts (b)–(e) using samples of size n = 3. Comment on the effect of increasing the sample size.

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