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Chapter 9: Q.111 (page 555)

For Americans using library services, the American Library Association claims that at most 67% of patrons borrow books. The library director in Owensboro, Kentucky feels this is not true, so she asked a local college statistic class to conduct a survey. The class randomly selected 100 patrons and found that 82 borrowed books. Did the class demonstrate that the percentage was higher in Owensboro, KY? Use 伪 = 0.01 level of significance. What is the possible proportion of patrons that do borrow books from the Owensboro Library?

Short Answer

Expert verified

CI: (0.7447, 0.8953)

Step by step solution

01

state the null and alternate hypothesis. we have to conduct hypothesis test if American using library services take more than 67% of patrons to borrow books according to American Library Association, on average. 

H0:p鈮�0.67Ha:p>0.67

02

Calculate the p-value using the normal distribution for proportions: 

p-value = 0.0007

In one to two complete sentences, explain what the p-value means for this problem. If the null hypothesis is true (the proportion is 0.67), then there is a 0.0007 probability that the sample (estimated) proportion is 0.82 or more.

03

Compare α and the p-value:Indicate the correct decision (“reject” or “do not reject” the null hypothesis), the reason for it, and write an appropriate conclusion, using complete sentences.

alphadecisionreason for decision
0.01Reject the null hypothesis.
p-value<0.01

Conclusion: At the 1% significance level, there is enough evidence to conclude that the proportion of patrons in Owensboro, KY who borrow books is more than 0.67. The class demonstrated that the percentage was higher than 67%.

04

Confidence interval and true proportion

To determine the possible proportion of patrons who do borrow books, construct a 95% confidence interval. It is (0.7447, 0.8953). We are 95% confident that the true population proportion of patrons in Owensboro, KY who borrow books is between 0.7447 and 0.8953 (between 74.47% and 89.53%).

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Most popular questions from this chapter

Over the past few decades, public health officials have examined the link between weight concerns and teen girls' smoking. Researchers surveyed a group of 273 randomly selected teen girls living in Massachusetts (between 12 and 15 years old). After four years the girls were surveyed again. Sixty-three said they smoked to stay thin. Is there good evidence that more than thirty percent of the teen girls smoke to stay thin?

After conducting the test, your decision and conclusion are

a. Reject H0: There is sufficient evidence to conclude that more than 30% of teen girls smoke to stay thin.

b. Do not reject H0: There is not sufficient evidence to conclude that less than 30% of teen girls smoke to stay thin.

c. Do not reject H0: There is not sufficient evidence to conclude that more than 30% of teen girls smoke to stay thin.

d. Reject H0: There is sufficient evidence to conclude that less than 30% of teen girls smoke to stay thin.

State the Type I and Type II errors in complete sentences given the following statements.

a. The mean number of years Americans work before retiring is 34.

b. At most 60% of Americans vote in presidential elections.

c. The mean starting salary for San Jose State University graduates is at least \(100,000 per year.

d. Twenty-nine percent of high school seniors get drunk each month.

e. Fewer than 5% of adults ride the bus to work in Los Angeles.

f. The mean number of cars a person owns in his or her lifetime is not more than ten.

g. About half of Americans prefer to live away from cities, given the choice.

h. Europeans have a mean paid vacation each year of six weeks.

i. The chance of developing breast cancer is under 11% for women.

j. Private universities mean tuition cost is more than \)20,000 per year.

We want to test if it takes fewer than 45minutes to teach a lesson plan. State the null and alternative hypotheses. Fill in the correct symbol (=,鈮�,鈮�,鈮�,鈮�,>)for the null and alternative hypotheses.

a.H0:渭-45

b.Ha:渭-45

A report by the Gallup Poll found that a woman visits her doctor, on average, at most5.8times each year. A random sample of 20women results in these yearly visit totals

3;2;1;3;7;2;9;4;6;6;8;0;5;6;4;2;1;3;4;1

At the 伪 = 0.05 level can it be concluded that the sample mean is higher than 5.8visits per year?

Suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is 2.5years. A study was then done to see if the meantime has increased in the new century. A random sample of 26first-time convicted burglars in a recent year was picked. The mean length of time in jail from the survey was 3years with a standard deviation of 1.8years. Suppose that it is somehow known that the population standard deviation is 1.5. If you were conducting a hypothesis test to determine if the mean length of jail time has increased, what would the null and alternative hypotheses be? The distribution of the population is normal.

a.Ho_______
b.Ha_______
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