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Introductory Statistics

Barbara Illowsky, Susan Dean

$Math Studyset Vaia Explanations$ Math

OER 2018 Edition · 902 pages

ISBN: 9781938168208

Chapter 9: Q. 9.13 (page 516)

$H_{0} : p = 0.5, H_{a} : p \neq 0.5$
Assume the $p$ -value is $0.2564$ . What type of test is this? Draw the picture of the p-value.

Short Answer

Expert verified

The alternative hypothesis $H_{a}$ shows that the test is two-tailed.

Step by step solution

Given Information

Test of a single population proportion is

$H_{0} : p = 0.5,$ against $H_{a} : p \neq 0.5 .$

The alternative hypothesis $H_{a}$ tells as the test is two-tailed.

We assume the $p$ -value is $0.2564$ .

Graph

So, the graph of the $p$ -value is as follows:

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Most popular questions from this chapter

Previously, an organization reported that teenagers spent $4.5$ hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was $4.75$ hours with a sample standard deviation of $2.0$ . Conduct a hypothesis test, the Type I error is:

a. to conclude that the current mean hours per week is higher than $4.5$ , when in fact, it is higher

b. to conclude that the current mean hours per week is higher than $4.5$ , when in fact, it is the same

c. to conclude that the mean hours per week currently is $4.5$ , when in fact, it is higher

d. to conclude that the mean hours per week currently is no higher than $4.5$ , when in fact, it is not higher

The student academic group on a college campus claims that freshman students study at least $2.5$ hours per day, on average. One Introduction to Statistics class was skeptical. The class took a random sample of $30$ freshman students and found a mean study time of $137$ minutes with a standard deviation of $45$ minutes. At $α = 0.01$ level, is the student academic group’s claim correct?

In $1955$ , Life Magazine reported that the $25$ year-old mother of three worked, on average, an $80$ hour week. Recently,

many groups have been studying whether or not the women's movement has, in fact, resulted in an increase in the average

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standard deviation was ten. Does it appear that the mean work week has increased for women at the role="math" localid="1650381098713" $5 %$ level?

Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test. At a significance level of a = 0.05, what is the correct conclusion?

a. There is enough evidence to conclude that the mean number of hours is more than 4.75

b. There is enough evidence to conclude that the mean number of hours is more than 4.5

c. There is not enough evidence to conclude that the mean number of hours is more than 4.5

d. There is not enough evidence to conclude that the mean number of hours is more than 4.75

According to the Center for Disease Control website, in $2011$ at least $18 %$ of high school students have smoked a cigarette. An Introduction to Statistics class in Davies County,KY conducted a hypothesis test at the local high school (a medium sized–approximately $1, 200$ students–small city demographic) to determine if the local high school’s percentage was lower. One hundred fifty students were chosen at random and surveyed. Of the $150$ students surveyed, $82$ have smoked. Use a significance level of $0.05$ and using appropriate statistical evidence, conduct a hypothesis test and state the conclusions.

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$H_{0} : p = 0.5, H_{a} : p \neq 0.5$
Assume the $p$ -value is $0.2564$ . What type of test is this? Draw the picture of the p-value.

Short Answer

Step by step solution

Given Information

Graph

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H0:p=0.5,Ha:p≠0.5Assume the p-value is 0.2564. What type of test is this? Draw the picture of the p-value.

Short Answer

Step by step solution

Given Information

Graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Mechanics Maths

Statistics

Pure Maths

Geometry

Applied Mathematics

Study anywhere. Anytime. Across all devices.

$H_{0} : p = 0.5, H_{a} : p \neq 0.5$
Assume the $p$ -value is $0.2564$ . What type of test is this? Draw the picture of the p-value.