Question

students at a major university believe they can save money buying textbooks online rather than at the local bookstores. in order to test this theory, they randomly sampled 25 textbooks on the shelves of the local bookstores. the students then found the best available price for the same textbooks via online retailers. the prices for the textbooks are listed in the following table. based on the data, is it less expensive for the students to purchase textbooks from the online retailers than from local bookstores? use α = 0.05. let prices at local bookstores represent population 1 and prices at online retailers represent population 2. table of textbook prices (dollars) with columns textbook, bookstore, online retailer, etc. step 1 of 3: state the null and alternative...

Explanation:

Step1: Define Hypotheses

We are testing if online prices (Population 2) are less than local prices (Population 1). Let \( d = \text{Population 1 - Population 2} \) (local - online).
Null hypothesis (\( H_0 \)): There is no difference or online is not cheaper, so \( \mu_d \leq 0 \) (or \( \mu_{\text{local}} \leq \mu_{\text{online}} \)).
Alternative hypothesis (\( H_1 \)): Online is cheaper, so \( \mu_d > 0 \) (or \( \mu_{\text{local}} > \mu_{\text{online}} \)), which is equivalent to testing if \( \mu_{\text{online}} < \mu_{\text{local}} \), so \( H_1: \mu_2 < \mu_1 \) (or \( \mu_d = \mu_1 - \mu_2 > 0 \)).

In terms of \( d \) (local - online), the hypotheses are:
\( H_0: \mu_d \leq 0 \)
\( H_1: \mu_d > 0 \)

Answer:

Null hypothesis: \( H_0: \mu_d \leq 0 \) (or \( H_0: \mu_{\text{local}} \leq \mu_{\text{online}} \))
Alternative hypothesis: \( H_1: \mu_d > 0 \) (or \( H_1: \mu_{\text{local}} > \mu_{\text{online}} \) or \( H_1: \mu_{\text{online}} < \mu_{\text{local}} \))

(Note: For paired t - test, defining \( d=\text{local - online} \), the hypotheses about \( \mu_d \) are \( H_0: \mu_d \leq 0 \) and \( H_1: \mu_d > 0 \) to test if online is cheaper (so local - online is positive on average).)