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Construct a 95%confidence interval for the population mean time spent waiting. State the confidence interval, sketch the graph, and calculate the error bound .

Short Answer

Expert verified

The error bound for mean is 0.12

The graph is

Step by step solution

01

Given information

Given in the question that , A hospital is trying to cut down on emergency room wait times. It is interested in the amount of time patients must wait before being called back to be examined. An investigation committee randomly surveyed 70patients. The sample mean was 1.5hours with a sample standard deviation of 0.5hours.

02

Explanation

The sample mean is x=1.5

The random sample is, n=70

The sample standard deviation iss=0.5

Now calculate the confidence interval using TI-83calculator using the steps given below,

Press STAT and use the arrow (?) to TESTS.

Then press the arrow()to 8 : TInterval and press enter.

Next, use the arrow ()to STARTS and press enter.

Then, press the arrow(?)and enter the inputs as shown below,

Step 5: Then press the arrow(?)to calculator and press enter. The output is given below,

03

Calculate the error bound 

The 95%confidence interval for the population mean time spent waiting is [1.38,1.62]

The graph is given below,

The error bound is calculated using the formula given below,

EBM=(Upper boundlower bound)2

The calculation is given below,

EBM=(1.621.38)2

localid="1648455872595" =0.242

=0.12

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Most popular questions from this chapter

In six packages of 鈥淭he Flintstones庐 Real Fruit Snacks鈥 there were five Bam-Bam snack pieces. The total number of snack pieces in the six bags was 68.We wish to calculate a 96%confidence interval for the population proportion of Bam-Bam snack pieces.

a. Define the random variables XandPin words.

b. Which distribution should you use for this problem? Explain your choice

c. Calculatep.

d. Construct a 96%confidence interval for the population proportion of Bam-Bam snack pieces per bag.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

e. Do you think that six packages of fruit snacks yield enough data to give accurate results? Why or why not?

A random survey of enrollment at 35 community colleges across the United States yielded the following figures:

6,414; 1,550; 2,109; 9,350; 21,828; 4,300; 5,944; 5,722; 2,825; 2,044; 5,481; 5,200; 5,853; 2,750; 10,012; 6,357; 27,000;

9,414; 7,681; 3,200; 17,500; 9,200; 7,380; 18,314; 6,557; 13,713; 17,768; 7,493; 2,771; 2,861; 1,263; 7,285; 28,165; 5,080;

11,622. Assume the underlying population is normal.

a. i.x- = __________

ii. sx = __________

iii. n = __________

iv. n 鈥 1 = __________

b. Define the random variables X and X-in words.

c. Which distribution should you use for this problem? Explain your choice.

d. Construct a 95% confidence interval for the population mean enrollment at community colleges in the United

States.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

e. What will happen to the error bound and confidence interval if 500 community colleges were surveyed? Why?

A random sample of statistics students were asked to estimate the total number of hours they spend watching television in an average week. The responses are recorded in Table 8.4. Use this sample data to construct a 98% confidence interval for the mean number of hours statistics students will spend watching television in one week.

0
3
1
20
9
5
10
1
10
4
14
2
4
4
5

Table8.4

Suppose we have data from a sample. The sample mean is 15, and the error bound for the mean is 3.2. What is the confidence interval estimate for the population mean?

A poll of 1,200 voters asked what the most significant issue was in the upcoming election. Sixty-five percent answered the economy. We are interested in the population proportion of voters who feel the economy is the most important.

Construct a 90% confidence interval, and state the confidence interval and the error bound.

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