Elementary Statistics: Picturing the World

Ron Larson, Betsy Farber

Chapter 7 Hypothesis Testing with Dna Sample - all with Video Answers

Educators

Section 1

Introduction to Hypothesis Testing

00:29

Problem 1

What are the two types of hypotheses used in a hypothesis test? How are they related?

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00:38

Problem 2

Describe the two types of errors possible in a hypothesis test decision.

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00:34

Problem 3

What are the two decisions that you can make from performing a hypothesis test?

Harsh Gadhiya

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00:36

Problem 4

Does failing to reject the null hypothesis mean that the null hypothesis is true? Explain.

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00:19

Problem 5

True or False?Determine whether the statement is true or false. If it is false, rewrite it as a true statement.
In a hypothesis test, you assume the alternative hypothesis is true.

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00:26

Problem 6

True or False?Determine whether the statement is true or false. If it is false, rewrite it as a true statement.
A statistical hypothesis is a statement about a sample.

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00:16

True or False?Determine whether the statement is true or false. If it is false, rewrite it as a true statement.
If you decide to reject the null hypothesis, then you can support the alternative hypothesis.

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00:33

Problem 8

True or False?Determine whether the statement is true or false. If it is false, rewrite it as a true statement.
The level of significance is the maximum probability you allow for rejecting a null hypothesis when it is actually true.

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00:15

Problem 9

True or False?Determine whether the statement is true or false. If it is false, rewrite it as a true statement.
A large $P$ -value in a test will favor rejection of the null hypothesis.

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00:14

Problem 10

True or False?Determine whether the statement is true or false. If it is false, rewrite it as a true statement.
To support a claim, state it so that it becomes the null hypothesis.

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00:47

Problem 11

The statement represents a claim. Write its complement and state which is $H_{0}$ and which is $H_{a}$.
$$\mu \leq 645$$

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00:15

Problem 12

The statement represents a claim. Write its complement and state which is $H_{0}$ and which is $H_{a}$.
$$\mu < 128$$

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00:18

Problem 13

The statement represents a claim. Write its complement and state which is $H_{0}$ and which is $H_{a}$.
$$\sigma \neq 5$$

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00:29

Problem 14

The statement represents a claim. Write its complement and state which is $H_{0}$ and which is $H_{a}$.
$$\sigma^{2} \geq 1.2$$

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00:29

Problem 15

The statement represents a claim. Write its complement and state which is $H_{0}$ and which is $H_{a}$.
$$p<0.45$$

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00:24

Problem 16

The statement represents a claim. Write its complement and state which is $H_{0}$ and which is $H_{a}$.
$$p=0.21$$

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00:52

Problem 17

Match the alternative hypothesis with its graph. Then state the null hypothesis and sketch its graph.
$$H_{a}: \mu > 3$$

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00:29

Problem 18

Match the alternative hypothesis with its graph. Then state the null hypothesis and sketch its graph.
$$H_{a}: \mu < 3$$

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00:19

Problem 19

Match the alternative hypothesis with its graph. Then state the null hypothesis and sketch its graph.
$$H_{a}: \mu \neq 3$$

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00:22

Problem 20

Match the alternative hypothesis with its graph. Then state the null hypothesis and sketch its graph.
$$H_{a}: \mu > 2$$

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00:27

Problem 21

Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.
$$\begin{aligned}
&H_{0}: \mu \leq 8.0\\
&H_{a}: \mu > 8.0
\end{aligned}$$

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00:24

Problem 22

Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.
$$\begin{aligned}
&H_{0}: \sigma \geq 5.2\\
&H_{a}: \sigma < 5.2
\end{aligned}$$

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00:43

Problem 23

Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.
$$\begin{aligned}
&H_{0}: \sigma^{2}=142\\
&H_{a}: \sigma^{2} \neq 142
\end{aligned}$$

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00:32

Problem 24

Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.
$$\begin{aligned}
&H_{0}: p=0.25\\
&H_{a}: p \neq 0.25
\end{aligned}$$

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00:48

Problem 25

Write the claim as a mathematical statement. State the null and alternative hypotheses, and identify which represents the claim.
A laptop manufacturer claims that the mean life of the battery for a certain model of laptop is more than 6 hours.

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00:36

Problem 26

Write the claim as a mathematical statement. State the null and alternative hypotheses, and identify which represents the claim.
As stated by a company's shipping department, the number of shipping errors per million shipments has a standard deviation that is less than 3.

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00:18

Problem 27

Write the claim as a mathematical statement. State the null and alternative hypotheses, and identify which represents the claim.
The standard deviation of the base price of a certain type of all-terrain vehicle is no more than $\$ 320$.

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00:47

Problem 28

Write the claim as a mathematical statement. State the null and alternative hypotheses, and identify which represents the claim.
An amusement park claims that the mean daily attendance at the park is at least 20,000 people.

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00:38

Problem 29

Write the claim as a mathematical statement. State the null and alternative hypotheses, and identify which represents the claim.
A company claims that its brands of paint have a mean drying time of less than 45 minutes.

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00:57

Problem 30

Write the claim as a mathematical statement. State the null and alternative hypotheses, and identify which represents the claim.
According to a recent survey, $39 \%$ of college students own a credit card.

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01:43

Problem 31

Describe type I and type II errors for a hypothesis test of the indicated claim.
A furniture store claims that at least $60 \%$ of its new customers will return to buy their next piece of furniture.

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00:43

Problem 32

Describe type I and type II errors for a hypothesis test of the indicated claim.
A garden hose manufacturer advertises that the mean flow rate of a certain type of hose is 16 gallons per minute.

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01:09

Problem 33

Describe type I and type II errors for a hypothesis test of the indicated claim.
A local chess club claims that the length of time to play a game has a standard deviation of more than 12 minutes.

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01:10

Problem 34

Describe type I and type II errors for a hypothesis test of the indicated claim.
A researcher claims that the percentage of adults in the United States who own a video game system is not $26 \%$.

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00:58

Problem 35

Describe type I and type II errors for a hypothesis test of the indicated claim.
A police station publicizes that at most $20 \%$ of applicants become police officers.

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00:54

Problem 36

Describe type I and type II errors for a hypothesis test of the indicated claim.
A computer repairer advertises that the mean cost of removing a virus infection is less than $\$ 100 .$

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01:29

Problem 37

State $H_{0}$ and $H_{a}$ in words and in symbols. Then determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. Explain your reasoning.
A security expert claims that at least $14 \%$ of all homeowners have a home security alarm.

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01:01

Problem 38

State $H_{0}$ and $H_{a}$ in words and in symbols. Then determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. Explain your reasoning.
A manufacturer of grandfather clocks claims that the mean time its clocks lose is no more than 0.02 second per day.

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01:01

Problem 39

State $H_{0}$ and $H_{a}$ in words and in symbols. Then determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. Explain your reasoning.
A golf analyst claims that the standard deviation of the 18 -hole scores for a golfer is less than 2.1 strokes.

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00:49

Problem 40

State $H_{0}$ and $H_{a}$ in words and in symbols. Then determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. Explain your reasoning.
A report claims that $87 \%$ of lung cancer deaths are due to tobacco use.

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00:48

Problem 41

State $H_{0}$ and $H_{a}$ in words and in symbols. Then determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. Explain your reasoning.
A baseball team claims that the mean length of its games is less than 2.5 hours.

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00:47

Problem 42

State $H_{0}$ and $H_{a}$ in words and in symbols. Then determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. Explain your reasoning.
A state claims that the mean tuition of its universities is no more than $\$ 25,000$ per year.

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01:25

Problem 43

Determine whether the claim represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that
(a) rejects the null hypothesis?
(b) fails to reject the null hypothesis?
A scientist claims that the mean incubation period for swan eggs is less than 40 days.

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01:09

Problem 44

Determine whether the claim represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that
(a) rejects the null hypothesis?
(b) fails to reject the null hypothesis?
A government agency claims that more than $75 \%$ of full-time workers earn over $\$ 538$ per week.

Harsh Gadhiya

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01:02

Problem 45

Determine whether the claim represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that
(a) rejects the null hypothesis?
(b) fails to reject the null hypothesis?
A researcher claims that the standard deviation of the life of a certain type of lawn mower is at most 2.8 years.

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01:15

Problem 46

Determine whether the claim represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that
(a) rejects the null hypothesis?
(b) fails to reject the null hypothesis?
An automotive manufacturer claims that the standard deviation for the gas mileage of its models is 3.9 miles per gallon.

Harsh Gadhiya

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00:50

Problem 47

Determine whether the claim represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that
(a) rejects the null hypothesis?
(b) fails to reject the null hypothesis?
A researcher claims that less than $16 \%$ of people had no health care visits in the past year.

Harsh Gadhiya

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00:46

Problem 48

Determine whether the claim represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that
(a) rejects the null hypothesis?
(b) fails to reject the null hypothesis?
A sports drink maker claims that the mean calorie content of its beverages is 72 calories per serving.

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00:49

Problem 49

Your medical research team is investigating the mean cost of a 30 -day supply of a certain heart medication.
A pharmaceutical company thinks that the mean cost is less than $\$ 60 .$ You want to support this claim. How would you write the null and alternative hypotheses?

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00:35

Problem 50

A taxicab company claims that the mean travel time between two destinations is about 21 minutes. You work for the bus company and want to reject this claim. How would you write the null and alternative hypotheses?

Harsh Gadhiya

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01:22

Problem 51

A refrigerator manufacturer claims that the mean life of its competitor's refrigerators is less than 15 years. You are asked to perform a hypothesis test to test this claim. How would you write the null and alternative hypotheses when
(a) you represent the manufacturer and want to support the claim?
(b) you represent the competitor and want to reject the claim?

Harsh Gadhiya

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01:11

Problem 52

An Internet provider is trying to gain advertising deals and claims that the mean time a customer spends online per day is greater than 28 minutes. You are asked to test this claim. How would you write the null and alternative hypotheses when
(a) you represent the Internet provider and want to support the claim?
(b) you represent a competing advertiser and want to reject the claim?

Harsh Gadhiya

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00:50

Problem 53

Why can decreasing the probability of a type I error cause an increase in the probability of a type II error?

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00:53

Problem 54

Explain why a level of significance of $\alpha=0$ is not used.

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00:47

Problem 55

A null hypothesis is rejected with a level of significance of 0.05. Is it also rejected at a level of significance of 0.10? Explain.

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01:01

Problem 56

A null hypothesis is rejected with a level of significance of 0.10. Is it also rejected at a level of significance of $0.05 ?$ Explain.

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02:00

Problem 57

You are given a null hypothesis and three confidence intervals that represent three samplings. Determine whether each confidence interval indicates that you should reject $H_{0} .$ Explain your reasoning.

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01:52

Problem 58

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01:34

Problem 59

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01:56

Problem 60

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