Math Problem Statement

A researcher hypothesizes that the average student spends less than 20% of their total study time reading the textbook. The appropriate hypothesis test is a left-tailed test for a population mean.

Solution

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extracted_text = pytesseract.image_to_string(img) extracted_textThe image contains a question asking whether the statement about the hypothesis test is true or false. Here's the content:

Question:
"A researcher hypothesizes that the average student spends less than 20% of their total study time reading the textbook. The appropriate hypothesis test is a left-tailed test for a population mean."

Options:

  • True
  • False

Analysis:

The researcher is hypothesizing that the mean (average) percentage of time spent reading the textbook is less than 20%. This suggests a left-tailed test because the alternative hypothesis is that the population mean is less than a specified value (in this case, 20%).

In hypothesis testing:

  • A left-tailed test is used when the hypothesis predicts that the population parameter (mean) will be less than a certain value.
  • The null hypothesis typically states that the mean is equal to or greater than the specified value, and the alternative hypothesis states that the mean is less than that value.

Given this reasoning, the appropriate hypothesis test is indeed a left-tailed test for a population mean. Therefore, the correct answer is:

True.

Would you like further details on hypothesis testing or how to set up the hypothesis? Let me know if you need more assistance!

Here are some related questions for you:

  1. What is the difference between a left-tailed and right-tailed hypothesis test?
  2. How do you formulate the null and alternative hypotheses for this situation?
  3. What is the significance of the alpha level in hypothesis testing?
  4. How do you calculate the p-value for a left-tailed test?
  5. What are the common errors in hypothesis testing (Type I and Type II)?

Tip: Always define your hypotheses clearly before performing a hypothesis test, and make sure to select the correct type of test based on your research question.

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Math Problem Analysis

Mathematical Concepts

Hypothesis Testing
Population Mean

Formulas

z-test formula
t-test formula for population mean

Theorems

Central Limit Theorem

Suitable Grade Level

Grades 11-12 or Undergraduate Statistics