# Question

The Wall Street Journal reported that the age at first startup for 55% of entrepreneurs was 29 years of age or less and the age at first startup for 45% of entrepreneurs was 30 years of age or more (The Wall Street Journal, March 19, 2012).

a. Suppose a sample of 200 entrepreneurs will be taken to learn about the most important qualities of entrepreneurs. Show the sampling distribution of ṕ where ṕ is the sample proportion of entrepreneurs whose first startup was at 29 years of age or less.

b. What is the probability that the sample proportion in part (a) will be within ± .05 of its population proportion?

c. Suppose a sample of 200 entrepreneurs will be taken to learn about the most important qualities of entrepreneurs. Show the sampling distribution of ṕ where ṕ is now the sample proportion of entrepreneurs whose first startup was at 30 years of age or more.

d. What is the probability that the sample proportion in part (c) will be within ±.05 of its population proportion?

e. Is the probability different in parts (b) and (d)? Why?

f. Answer part (b) for a sample of size 400. Is the probability smaller? Why?

a. Suppose a sample of 200 entrepreneurs will be taken to learn about the most important qualities of entrepreneurs. Show the sampling distribution of ṕ where ṕ is the sample proportion of entrepreneurs whose first startup was at 29 years of age or less.

b. What is the probability that the sample proportion in part (a) will be within ± .05 of its population proportion?

c. Suppose a sample of 200 entrepreneurs will be taken to learn about the most important qualities of entrepreneurs. Show the sampling distribution of ṕ where ṕ is now the sample proportion of entrepreneurs whose first startup was at 30 years of age or more.

d. What is the probability that the sample proportion in part (c) will be within ±.05 of its population proportion?

e. Is the probability different in parts (b) and (d)? Why?

f. Answer part (b) for a sample of size 400. Is the probability smaller? Why?

## Answer to relevant Questions

People end up tossing 12% of what they buy at the grocery store (Reader’s Digest. March 2009). Assume this is the true population proportion and that you plan to take a sample survey of 540 grocery shoppers to further ...U.S. News & World Report publishes comprehensive information on America’s best colleges (America’s Best Colleges, 2009 ed.). Among other things, they provide a listing of their 133 best national universities. You would ...A production process is checked periodically by a quality control inspector. The inspector selects simple random samples of 30 finished products and computes the sample mean product weights x. If test results over a long ...Data were collected on the amount spent by 64 customers for lunch at a major Houston restaurant. These data are contained in the file named Houston. Based on past studies the population standard deviation is known with σ = ...How large a sample should be selected to provide a 95% confidence interval with a margin of error of 10? Assume that the population standard deviation is 40.Post your question

0