Question

c) Smaller than the population mean. d) Cannot be determined from this information 12. of each sample is determined. As the sample size n becomes increasingly large, what distribution does the distribution approach? All possible samples of size n are selected from a population and the mean a) normal distribution b) binomial distribution c) sampling distribution d) uniform distribution 13. Suppose the mean height of American men (ages 20-29) is 68.2 inches, with standard deviation ?-2.7 inches. If these heights are normally distributed, are you more likely to randomly select one man with a height less than 66 inches or are you more likely to select a sample of 15 men with a height less than 66 inches? Explain. (4 pt.) 14. Two samples were taken to determine the popularity rating of the mayor of New York City. The 95% confidence intervals for the population proportions are listed belo hich sample had more respondents (larger sample size)? Explain. (4 pt.) Sample I: (0.4925, 0.5325) Sample II: (0.4842, 0.5412)

Answer 1

12) Option - d) normal distribution.

13) For randomly select of one man

P(X < 66)

= P((X - $\mu$ )/ $\sigma$ < (66 - $\mu$ )/ $\sigma$ )

= P(Z < (66 - 68.2)/2.7)

= P(Z < -0.81)

= 0.2090

For 15 randomly selected man

P( $\bar x$ < 66)

= P(( $\bar x$ - $\mu$ )/( $\sigma$ / $\sqrt n$ < (66 - $\mu$ )/( $\sigma$ / $\sqrt n$ )

= P(Z < (66 - 68.2)/(2.7/sqrt(15)))

= P(Z < -3.16)

= 0.0008

As the probability for a randomly select one man is greater than 0.05, so it is more likely.

c) Sample II had more respondents.