1A study of 70 bolts of carpet showed that their average len

1.)A study of 70 bolts of carpet showed that their average length was 160 yards. The standard deviation of the population is 6 yards. Which of the following is the 90% confidence interval for the mean length per bolt of carpet?

2.)A report states that 44% of home owners had a vegetable garden. A college student decided to estimate the true proportion of home owners that have a vegetable garden. In a sample of 215 home owners the student recorded that 90 have a vegetable garden. Use this information to find a 90% confidence interval of the true proportion of home owners who have vegetable gardens.

3.)A research psychologist wants to estimate, with 99% confidence, the true proportion of college applicants who have parents that have remarried. How large a sample is needed to estimate the true proportion of students who have parents who have remarried to within 3.5%?

help with any of these would be great! thanks so much, math geniuses

Solution

Note that              
              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
              
X = sample mean =    160          
z(alpha/2) = critical z for the confidence interval =    1.644853627          
s = sample standard deviation =    6          
n = sample size =    70          
              
Thus,              
              
Lower bound =    158.8204143          
Upper bound =    161.1795857          
              
Thus, the confidence interval is              
              
(   158.8204143   ,   161.1795857   )

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