In: Statistics and Probability
1) In a random sample of 61 professional actors, 22 were
extroverts.
a. Comment on the requirements of a confidence interval. b. Find a
90% confidence interval for p.
2) If the average height x is calculated from a random sample of
135 adult Americans, find the probability that the mean height of
the sample is between 68 and 70 inches.
3) A food distributor is attempting to deal with complaints that an
unacceptable percentage of eggs transported by the company arrive
cracked. In a random sample of 325 eggs, 43 are found to be
cracked. Calculate a 99% confidence interval for the true
population proportion.
4) Suppose we will be computing a 90% confidence interval for a
population proportion. Determine the sample size required to
produce a margin of error of at most 3 percentage points.
a)as sample is random as well np=22 and n(1-p)=39 both are greater than equal to 10 , therefore requirements for the confidence interval are satisfied
b)
2)
for this mean and std deviation of heights are required
3)
4)
here margin of error E = | 0.0300 | |
for90% CI crtiical Z = | 1.645 | |
estimated proportion=p= | 0.5000 | |
required sample size n = | p*(1-p)*(z/E)2= | 752.00 |