# Question: The following data represent the ages of the winners of

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.

**View Solution:**## Answer to relevant Questions

The following data represent the running lengths (in minutes) of the winners of the Academy Award for Best Picture for the years 2004–2009. 2004: Million Dollar Baby ..... 132 2005: Crash ........... 112 2006: The Departed ...n = 500, p = 0.4 A simple random sample of size n = 1460 is obtained from a population whose size is N = 1,500,000 and whose population proportion with a speciﬁed characteristic is p = 0.42. (b) What is the probability of obtaining x = 657 ...sample proportion of adults who respond yes, is approximately normal, how many more adult Americans does the researcher need to sample if (a) 10% of all adult Americans support the changes? (b) 20% of all adult Americans ...In a survey of 35 adult Americans, it was found that the mean age (in years) that people would like to live to is 87.9 with a standard deviation of 15.5.An analysis of the raw data indicates the distribution is skewed ...Post your question