Math Problem Statement
One study claimed that 93% of college students identify themselves as procrastinators. A professor believes that the claim regarding college students is too high. The professor conducts a simple random sample of 194 college students and finds that 174 of them identify themselves as procrastinators. Does this evidence support the professor’s claim that fewer than 93% of college students are procrastinators? Use a 0.02 level of significance. Step 2 of 3 : Compute the value of the test statistic. Round your answer to two decimal places.
Solution
To compute the value of the test statistic, we follow these steps:
Step 1: Define the hypotheses
- Null Hypothesis (H₀): (The proportion of college students who identify as procrastinators is 93%.)
- Alternative Hypothesis (H₁): (The proportion of college students who identify as procrastinators is less than 93%.)
Step 2: Compute the sample proportion
The sample proportion is calculated as:
Step 3: Compute the standard error
The standard error is given by:
Step 4: Compute the test statistic
The test statistic is computed using the formula:
Thus, the value of the test statistic is approximately -1.81.
Would you like details on how to proceed with this hypothesis test, or have any other questions?
Here are five related questions you might consider:
- How do you find the p-value corresponding to this test statistic?
- What does the significance level of 0.02 mean in this context?
- How do you determine whether to reject the null hypothesis?
- What assumptions must be met for the use of a z-test in this scenario?
- How would the conclusion change if the significance level were different?
Tip: Always ensure the sample size is large enough when performing hypothesis tests, as smaller samples can lead to less reliable results.
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Math Problem Analysis
Mathematical Concepts
Hypothesis Testing
Proportion Estimation
Standard Error
Formulas
Standard Error formula: SE = sqrt((p * (1 - p)) / n)
Theorems
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Suitable Grade Level
Advanced College
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