Final answer:
Elijah's question about the mean price of sociology versus math and science books requires a hypothesis test to determine, using t-statistics and significance levels. Without calculations, we can't conclude whether sociology books are cheaper. Therefore, the correct answer choice is not provided based on the information given.
Step-by-step explanation:
Elijah wants to know if there is a significant difference in the mean prices of sociology books compared to math and science books from an online site. To determine this, a hypothesis test can be carried out using the sample mean and standard deviation values provided. As the sample sizes are both 33, which is more than 30, we can assume that the sampling distribution of the mean is approximately normal due to the Central Limit Theorem.
To test whether the mean price of a sociology book is lower than the mean price of a math or science book at the 1% significance level, we would perform a two-sample t-test for the means of two independent samples. However, the detailed procedure of the hypothesis test is not provided in this scenario. Typically, we would set up the null hypothesis stating that the mean prices of sociology books and math and science books are equal, and the alternative hypothesis would state that the mean price of sociology books is lower. A t-statistic would be calculated, and if this calculated t-statistic fell into the rejection region (usually, for a 1% significance level, it would be the lower tail of the distribution), we would reject the null hypothesis in favor of the alternative.
Without the full statistical analysis and calculation, we cannot conclusively answer whether option (a) or (b) is correct, and option (c) would be incorrect as 'b' contradicts 'a'. Option (d) is not correct as it is possible to test the hypothesis with the given data. Thus, we cannot determine the correct choice based solely on the information provided in the question. A statistical test is needed to make such a determination.