## Question

###### C) Smaller than the population mean. d) Cannot be determined from this information 12. of each...

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)

## Answers

12) Option - d) normal distribution.

13) For randomly select of one man

P(X < 66)

= P((X - )/ < (66 - )/)

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

= P(Z < -0.81)

= 0.2090

For 15 randomly selected man

P( < 66)

= P(( - )/(/ < (66 - )/(/)

= 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.

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