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Chapter 8: Q.9 (page 477)

Construct a 90% confidence interval for the population mean time to complete the forms. State the confidence interval, sketch the graph and calculate the error bound.

Short Answer

Expert verified

The confidence interval isCl:(7.9441,8.4559).

Step by step solution

01

Given Information

90% confidence interval for the population mean time to complete the forms.

02

Explanation

Let's calculate the Margin of error by using the given formula:

Za2脳蟽n

Place the values=Z0.102脳2.2200=1.6449脳2.2200=0.25588

Then we have to find the confidence interval by using the given formula:

X炉卤Za2脳蟽n

role="math" localid="1652508772667" Confidence Interval=8.2卤Z0.102脳2.2200=8.2卤1.6449脳2.2200=[7.944,8.455]

Therefore, the confidence interval Cl:(7.9441,8.4559).

The graph:

The error bound EBM=0.26.

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Most popular questions from this chapter

The U.S. Census Bureau conducts a study to determine the time needed to complete the short form. The Bureau surveys 200 people. The sample mean is 8.2 minutes. There is a known standard deviation of 2.2 minutes. The population distribution is assumed to be normal.

Identify the following:

a. x炉 = _____

b. 蟽 = _____

c. n = _____

The mean age for all Foothill College students for a recent Fall term was 33.2. The population standard deviation has been pretty consistent at 15. Suppose that twenty-five Winter students were randomly selected. The mean age for the sample was 30.4. We are interested in the true mean age for Winter Foothill College students. Let X=the age of a Winter Foothill College student.

In words, define the random variable X炉.

120. An article regarding interracial dating and marriage recently appeared in the Washington Post. Of the1,709randomly selected adults, 315identified themselves as Latinos, 323 identified themselves as blacks, 254identified themselves as Asians, and 779identified themselves as whites. In this survey, 86%of blacks said that they would welcome a white person into their families. Among Asians, 77%would welcome a white person into their families, 71%would welcome a Latino, and 66%would welcome a black person.

a. We are interested in finding the 95%confidence interval for the percent of all black adults who would welcome a white person into their families. Define the random variables role="math" localid="1650173946070" Xand P', in words.

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

c. Construct a 95% confidence interval.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

The average height of young adult males has a normal distribution with a standard deviation of 2.5 inches. You want to estimate the mean height of students at your college or university to within one inch with 93 per cent confidence. How many male students must you measure?

In a recent sample of 84used car sales costs, the sample mean was \(6,425with a standard deviation of \)3,156. Assume

the underlying distribution is approximately normal.

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

b. Define the random variableXin words.

c. Construct a 95%confidence interval for the population mean cost of a used car.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

d. Explain what a 鈥�95% confidence interval鈥� means for this study.
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