1) What proportion of all Americans believe the president is doing a good job? A recent poll found that 39% of 1000 randomly selected Americans approved of the way George W. Bush is handling his job as president.

 

a) Does this mean that only 39% of all Americans approve of the way George W. Bush is handling his job as president?

b) For a sample proportion, as long as the population is greater than ten times the sample size, we can approximate the standard deviation to be square root p(1-P)/n What is the standard deviation for this sample?  

c) What is the critical value for a 90% confidence interval?

d) What is the critical value for a 95% confidence interval?

e) What is the 90% confidence interval? Be sure to include the formula with your numbers plugged in. Use the model:p+ or -z  x  square root p(1-P)/n

f) What is the 95% confidence interval?

2) You measure the weights of 24 male runners. You do not actually choose an SRS, but you are willing to assume that these runners are a random sample from the population of male runners in your town or city. Here are their weights in kilograms:

67.8 61.9 63.0 53.1 62.3 59.7 55.4 58.9
60.9 69.2 63.7 68.3 64.7 65.6 56.0 57.8
66.0 62.9 53.6 65.0 55.8 60.4 69.3 61.7

a) Suppose that the standard deviation of the population is known to be sigma = 4.5 kg. What is sx, the standard error of x?
b) Give a 95% confidence interval for the mean of the population from which the sample is drawn.
c) Are you quite sure that the average weight of the population of runners is less than 65 kg?

3) What is the mean number of hours that high school students spend on homework per week? It is known that the standard deviation of the population is 2.2 hours. In a random sample of 40 students, it is found that they average 13 hours per week on homework.

a) What is the standard deviation for this sample?
b) What is the critical value for a 90% confidence interval?
c) What is the critical value for a 95% confidence interval?
d) What is the 90% confidence interval? Be sure to include the formula with your numbers plugged in. Use the model: x + or - z * σ/sqrt n
e) What is the 95% confidence interval?

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