Among various ethnic groups, the standard deviation of heights is known to be approximately three inches. We wish to construct a 95% confidence interval for the mean height of males from a certain country. Forty-eight males are surveyed from a particular country. The sample mean is71inches.The sample standard deviation is2.2inches.

Be careful with the rounding try to use all decimal places when needed

• Part (a)
• Find the following. (Enter exact numbers as integers, fractions, or decimals.)
• (i)x(with a line over it)=
• (ii)=
• (iii)n=

Part (b) Multiple choice

• In words, define the random variablesxandX (with a line over it).

a) xis the number of males in the study, andXis the number of males in this country.

b) xis the mean height from a sample of 48 males, andXis the height of a male from this country.

c) xis the number of males in this country, andXis the number of males in the study.

d) xis the height of a male from this country, andXis the mean height from a sample of 48 males.

• Part (c) Multiple choice
• Which distribution should you use for this problem? Explain your choice.

A) The Student'st-distribution should be used because the sample mean is smaller than 30.

b) The Student'st-distribution should be used because the sample standard deviation is given.

c) The standard normal distribution should be used because the population standard deviation is known.

D) The standard normal distribution should be used because the mean is given.

• Part (d)
• Construct a 95% confidence interval for the population mean height of males of this country.
• (i) State the confidence interval. (Round your answers to two decimal places.)
• (__________,___________)
• (ii) Sketch the graph.
• (iii) Calculate the error bound. (Round your answer to two decimal places.)

___________

• Part (e) Multiple Choice

What will happen to the level of confidence obtained if 1,000 males are surveyed instead of48? Why?

A) The confidence interval will increase in size, because an increase in sample size decreases variability, which means a larger interval will be needed to capture the true population mean.

B) The confidence interval will decrease in size, because an increase in sample size increases variability, which means a smaller interval will be enough to capture the true population mean.

C) The confidence interval will decrease in size, because an increase in sample size decreases variability, which means a smaller interval will be enough to capture the true population mean.

D) The confidence interval will increase in size, because an increase in sample size increases variability, which means a larger interval will be needed to capture the true population mean.