Question

research suggests that the pressure of being timed may interfere with performance on tests that involve mathematical problems. a fictional study was conducted with 30 sixth - graders. first, the sixth - graders were given a math test that contained 50 problems and were told that they had only one hour to complete it (timed condition). the same sixth - graders were later given a math test that contained 50 problems and were told that they could have as much time, as needed, to complete the test (unlimited time condition). the total number of correct answers for each sixth - grader was then calculated for each condition. then, for each student, the difference between the two scores (timed - untimed) was calculated. the researchers hypothesized that the sixth graders would get fewer correct answers when they took the test with a time limit than when they had unlimited time. the following hypotheses were tested: (h_0:mu_d = 0) (h_a:mu_d<0) the researchers analyzed the data and obtained the following output: summary statistics: |sample|n|mean|variance|std. dev.|std. err.| |---|---|---|---|---|---| |timed|50|35.3|41.438774|6.4372954|0.91037107| |untimed|50|38.7|41.030613|6.4055142|0.9058765| hypothesis test results: |difference|sample diff.|std. err.|df|t - stat|p - value| |---|---|---|---|---|---| |timed - untimed|-3.4|0.3736199|49|-9.100158|<0.0001| which of the following is an appropriate conclusion based on the output? a. the data do not provide sufficient evidence to reject (h_0). thus, the researchers conclude that sixth grade students get, on average, fewer correct answers and, thus, lower scores, on math tests, when taking them under timed conditions as compared to untimed conditions. b. the data do not provide sufficient evidence to reject (h_0). thus, based on the data, the researchers cannot conclude that mean number of correct answers on the math test for the timed condition is lower than for the untimed condition. c. the data provide sufficient evidence to reject (h_0). thus, based on the data the researchers cannot conclude that mean number of correct answers on the math test for the timed condition is lower than for the untimed condition. d. the data provide sufficient evidence to reject (h_0). thus, the researchers conclude that sixth grade students get, on average, fewer correct answers and thus lower scores on math tests when taking them under timed conditions as compared to untimed conditions.

Explanation:

Step1: Recall hypothesis - testing decision - rule

If the p - value is less than the significance level (commonly $\alpha = 0.05$), we reject the null hypothesis $H_0$.

Step2: Identify the p - value

The p - value from the hypothesis test results is $p<0.0001$. Since $p < 0.05$, we reject the null hypothesis $H_0:\mu_d = 0$.

Step3: Interpret the alternative hypothesis

The alternative hypothesis $H_a:\mu_d<0$ means that the mean number of correct answers in the timed condition is less than the mean number of correct answers in the untimed condition. When we reject $H_0$, we support $H_a$.

Answer:

D. The data provide sufficient evidence to reject $H_0$. Thus, the researchers conclude that sixth - grade students get, on average, fewer correct answers and thus lower scores on math tests when taking them under timed conditions as compared to untimed conditions.