Answer all the following questions completely and all work and steps should be shown to prove to understand the process.When possible, to answer using a complete sentence and offering explanation, please do so.

1.ACT, Inc. reported that 74% of 1644 randomly selected college freshmen returned to college the next year.

a.[4 pts] Construct and interpret a 90% confidence interval to estimate the retention rate for college freshmen.

b.[4 pts] Let's say they only need a 2% margin of error with the same level of confidence the following year. How many college freshmen must be surveyed?

c.[2 pts] If they increased their confidence level to 95%, would the confidence intervals get wider or narrower? Explain why.

2.[5 pts] A Gallup poll asked 1200 randomly chosen adults what they think the ideal number of children for a family is. Of this sample, 53% stated that they thought 2 children is the ideal number.

a.Check the conditions needed to form a confidence interval. Discuss each one in context.

b.Construct and interpret a 95% confidence interval for the proportion of all US adults that think 2 children is the ideal number.