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Chapter 8: Q 47. (page 523)

Prom totals Use your interval from Exercise 39 to construct and interpret a 90%

confidence interval for the total number of seniors planning to go to the prom.

Short Answer

Expert verified

There is 90%confidence that between462and618seniors in Tanya's school go to prom.

Step by step solution

01

Given Information

It is given that c=90%=0.90

x=36,n=50

For1-伪=0.90, using probabilityza/2=1.645

02

Construct and interpret confidence interval

Conditions are:

Random: As samples are selected randomly, it is satisfied.

Independent: Sample of 50seniors is less than 10%of all population of all seniors. This condition is met.

Normal: There are 36success and 50-36=14failures which are greater than 10.

All conditions are fulfilled.

Sample proportion is calculated as: p^=xn

=3650=0.72

Margin of Error: E=z伪/2脳p^(1-p^)n

=1.645脳0.72(1-0.72)50=0.1045

Confidence Interval: p^-E=0.72-0.1045=0.6155

p^+E=0.72+0.1045=0.8245

The confidence interval is(0.6155,0.8245).

As population consists of 750seniors,

750(0.6155)=461.625鈮�462

750(0.8245)=618.375鈮�618

There is 90%confidence that between462-618seniors that plan to go to prom.

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Most popular questions from this chapter

Suppose we want a 90% confidence interval for the average amount spent on books by freshmen in their first year at a major university. The interval is to have a margin of error of at most \(2. Based on last year鈥檚 book sales, we estimate that the standard deviation of the amount spent will be close to \)30. The number of observations required is closest to which of the following?

a. 25

b.30

c. 225

d. 609

e. 865

The student body president of a high school claims to know the names of at least 1000of the 1800 students who attend the school. To test this claim, the student government advisor randomly selects 100students and asks the president to identify each by name. The president successfully names only 46of the students.

a. Identify the population and parameter of interest.

b. Check conditions for constructing a confidence interval for the parameter.

c. Construct a 99%confidence interval for p.

d. Interpret the interval in context.

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How many pairs of shoes, on average, do female teens have? To find out, an AP Statistics class selected an SRS of 20female students from their school. Then they recorded the number of pairs of shoes that each student reported having. Here are the data:

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