Math Problem Statement

  Compute the value of the test statistic. Round your answer to three decimal places.

Compute the value of the test statistic. Round your answer to three decimal places.

Solution

The problem appears to involve performing a hypothesis test to compare prices of textbooks at bookstores (Population 1) and online retailers (Population 2). We are likely using a paired sample t-test since the same textbooks are priced at both locations. The null hypothesis H0H_0 would be that there is no significant difference in prices between bookstores and online retailers, and the alternative hypothesis H1H_1 is that prices are less expensive online.

Here are the steps to compute the test statistic for a paired t-test:

  1. Calculate the differences between the paired values (prices at bookstore minus prices at the online retailer).
  2. Compute the mean difference (dˉ\bar{d}).
  3. Compute the standard deviation of the differences (sds_d).
  4. Calculate the test statistic using the formula: t=dˉsd/nt = \frac{\bar{d}}{s_d / \sqrt{n}} where nn is the number of pairs (in this case, 25).

Let me now calculate this.The value of the test statistic is approximately t=1.314t = 1.314 (rounded to three decimal places).

Would you like a detailed explanation of how this was calculated, or do you have any other questions?

Here are five related questions to consider:

  1. What are the null and alternative hypotheses for this test?
  2. How do you interpret the result of a paired t-test?
  3. How would the test statistic change if there were more textbooks in the sample?
  4. How does changing the significance level (α\alpha) affect the test conclusion?
  5. What would be the next step after computing the test statistic?

Tip: Always check the assumptions of the t-test, such as normality of the differences, especially when the sample size is small.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Hypothesis Testing
Paired Sample t-Test
Statistics

Formulas

t = (mean difference) / (standard deviation of differences / sqrt(n))

Theorems

Central Limit Theorem
Student's t-distribution

Suitable Grade Level

College/University