91Ó°ÊÓ

Write the null and alternative hypotheses for each of the following examples. Determine if each is a case of a two-tailed, a left-tailed, or a right-tailed test. a. To test if the mean number of hours spent working per week by college students who hold jobs is different from 20 hours b. To test whether or not a bank's ATM is out of service for an average of more than 10 hours per month c. To test if the mean length of experience of airport security guards is different from 3 years d. To test if the mean credit card debt of college seniors is less than \(\$ 1000\) e. To test if the mean time a customer has to wait on the phone to speak to a representative of a mail-order company about unsatisfactory service is more than 12 minutes

Step by step solution

01

Identify the Null and Alternative Hypothesis for Scenario a

The null hypothesis (H0) is that the mean number of hours spent working per week by college students who hold jobs is equal to 20 hours. The alternative hypothesis (H1) is that the mean number of hours spent working per week by college students who hold jobs is not equal to 20 hours. Since we are testing if it is different from 20 hours, it means we are considering both less than and more than 20 hours. Therefore this is a two-tailed test.

02

Identify the Null and Alternative Hypothesis for Scenario b

The null hypothesis (H0) is that the bank's ATM is out of service for an average of less or equal to 10 hours per month. The alternative hypothesis (H1) is that the bank's ATM is out of service for an average of more than 10 hours per month. The emphasis is on more than 10 hours, thus it is a right-tailed test.

03

Identify the Null and Alternative Hypothesis for Scenario c

The null hypothesis (H0) is that the mean length of experience of airport security guards is equal to 3 years. The alternative hypothesis (H1) is that the mean length of experience of airport security guards is different from 3 years. Testing for difference means considering both less than and more than 3 years. Therefore this is a two-tailed test.

04

Identify the Null and Alternative Hypothesis for Scenario d

The null hypothesis (H0) is that the mean credit card debt of college seniors is equal to or more than $1000$. The alternative hypothesis (H1) is that the mean credit card debt of college seniors is less than $1000$. This is because the emphasis is on less than $1000$, so it is a left-tailed test.

05

Identify the Null and Alternative Hypothesis for Scenario e

The null hypothesis (H0) is that the mean time a customer has to wait on the phone to speak to a representative of a mail-order company about unsatisfactory service is less than or equal to 12 minutes. The alternative hypothesis (H1) is that the mean time a customer has to wait on the phone is more than 12 minutes. As it is mentioned 'more than 12 minutes', it is a right-tailed test.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Null Hypothesis

In hypothesis testing, the null hypothesis, denoted as \( H_0 \), is a statement that indicates no effect or no difference. It serves as a starting point that you assume is true until you have sufficient evidence to suggest otherwise. For example, when testing if the mean number of hours spent working per week by college students is 20 hours, the null hypothesis would state: "The mean number of hours spent working is 20 hours" (i.e., \( H_0: \mu = 20 \)). This hypothesis assumes that there is no change or effect from what is generally expected or specified.

Alternative Hypothesis

The alternative hypothesis, symbolized as \( H_1 \), is the statement you aim to provide evidence for. It suggests that there is an effect or difference from the null hypothesis. In hypothesis tests, it's crucial because it represents what we are trying to prove. For instance, if we want to demonstrate that college students work a different number of hours per week than 20, the alternative hypothesis would be \( H_1: \mu eq 20 \), indicating a deviation from the given mean of 20 hours.

Two-tailed Test

A two-tailed test is used when testing for differences in either direction from a specified value. It is appropriate when the alternative hypothesis is non-directional. In simpler terms, you test for the possibility of a relationship in both directions. For example, if investigating whether the average length of experience for security guards differs from 3 years, the null hypothesis might be \( H_0: \mu = 3 \), while the alternative hypothesis would be \( H_1: \mu eq 3 \). Here, the test examines if the mean is either less than or greater than 3 years.

Right-tailed Test

A right-tailed test is conducted when the alternative hypothesis states that a parameter is greater than the null hypothesis value. It's used to test whether an observed value is significantly higher than a specified value. For example, testing if the mean time customers wait is more than 12 minutes involves a right-tailed test. The hypotheses would be \( H_0: \mu \leq 12 \) and \( H_1: \mu > 12 \). The focus is only on whether the value is on the higher side of a specified threshold.

Left-tailed Test

In a left-tailed test, the alternative hypothesis indicates that the parameter is less than the null hypothesis value. This is useful when you're looking to see if an observed value is significantly less than a set point. For instance, if the concern is whether college seniors have a mean credit card debt of less than \( \$1000 \), this would be a left-tailed test. The hypotheses are \( H_0: \mu \geq 1000 \) and \( H_1: \mu < 1000 \). The test focuses on values that are lower than the specified figure.