Question

In: Statistics and Probability

In the survey of 1500 students for the united states age 18 and under, 1043 were...

In the survey of 1500 students for the united states age 18 and under, 1043 were concerned about how they would pay for college.

a) Find the mean and standard deviation of those concerned about financing college.

b) Construct a 90% confidence interval for the population proportions. Interpret your results.

c) Find the minimum sample size needed to estimate the population proportion at the 99% confidence level in order to ensure that the estimate is accurate within 4% of the population proportion.

Solutions

Expert Solution

a) Given: X = 1043, n = 1500

Sample proportion

Let X denote the random variable with the event of success being that the students are concerned about how they would pay for college.

Since, X has a binary outcome, with independent trials,

Using property of Binomial Distribution:

Mean and Standard Deviation of those concerned about financing college are 1043 and 18 respectively.

b) 90% CI for population proportion is given by the formula:

......(For 90% CI, Z = 1.645)

= (0.676,0.715)

90% confidence interval for the population proportions is (0.676,0.715). If repeated samples are drawn, the true proportion would lie within this interval 90 out of 100 times.

c) The Margin of error given is 0.04

.......(For 99% CI, Z = 2.58)

The minimum sample size needed to estimate the population proportion at the 99% confidence level in order to ensure that the estimate is accurate within 4% of the population proportion is about 881.

orchestra answered 1 year ago
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