1. According to recent study conducted by the Pew Research Center, 73% of US teens (ages 12 to 17) use Facebook. A random sample of 10 US teens is selected. Let the random variable X be the number of teens using Facebook.

 

1. a) Is X a binomial random variable? Explain:

 

• Does this scenario describe a random experiment with a fixed number of trials?                      If so, find  the number of trials, n
• Does each trial result in two complimentary possibilities? If so, identify the “success” event

 

• Are the trials independent?

 

If yes, find the probability of “success”, p

1. b) What is the probability that exactly 8 teens are using Facebook?

 

 

 

1. c) What is the probability that at least 8 teens are using Facebook?

 

 

 

 

 

2. According to a recent study, the mean height of women (ages 20 –29) in the United States is 64 inches with a standard deviation of 2.75 inches. Assume that height is normally distributed in this population.
3. What height represents the 65th percentile? (Round to the nearest tenth). Include a sketch.

 

 

 

 

 

1. Approximately what percentage of women in the United States (ages 20 –29) are taller than 65 inches? Include a sketch.

 

 

 

 

 

 

 

3. According to a recent study, the mean height of women (ages 20 –29) in the United States is 64 inches with a standard deviation of 2.75 inches. Assume that height is normally distributed in this population.

What is the probability that in a random sample of size 10 the sample mean is be greater than 65 inches? Include a sketch.

 

 

 

 

 

4. In a random sample of 50 US men (ages 20 –29), the mean height was 69.2 inches with a standard deviation of 3.5 inches.
5. Find and interpret the 90% confidence interval for the population mean.

 

 

 

 

 

1. If you increase the confidence level, will the confidence interval estimate be wider or narrower? Explain.

 

 

 

5. How large a sample do you need to obtain a 99% confidence interval estimate of the mean within the margin of error of 1 inch, assuming normal distribution and population standard deviation of 2.75 inches

 

 

6. The mean height of women (ages 40 –49) in the United States is 62.6 inches. In a random sample of 30 women (ages 20 –29) the mean height was 64 inches with the standard deviation of 1.2 inches. Is there enough evidence to conclude that US women are getting taller at the a = 0.1 significance level?

 

1. Identify the null (H₀) and the alternative hypothesis (H_a)

 

 

1. Make a sketch, shading the critical (rejection) region

 

 

1. Use t-table to find the critical value T_C and mark it on you sketch above
2. Calculate the test statistics T₀ and mark it on your sketch, above

 

1. Based on the above, make a decision to reject H₀ or fail to reject H₀

 

1. Draw a conclusion. Is there enough evidence to conclude that US women are getting taller at the a = 0.1 significance level?