Question: A researcher is interested in assessing whether background noise affects a student's ability to study effectively. To investigate this, they divide university students into two

A researcher is interested in assessing whether background noise affects a student's ability to study effectively. To investigate this, they divide university students into two groups: one group studies in a quiet room (the "quiet" group), and the other group studies in a room with a moderate level of background noise, such as caf sounds (the "noisy" group). Each group is given a set of math problems to solve within an hour. Each person's score on solving the math problems is recorded, then the following means and standard deviations were calculated for the scores for each group. Group Sample Mean Sample SD Sample Size QUIET 15 5 60 NOISY 12 5 60 The analyst decides to conduct a two sample t-test. The hypothesis test will be conducted using = 0.01 using the hypotheses below: H0: QUIET - NOISY = 0 HA: QUIET - NOISY 0,What is the critical value for this hypothesis test? Answer to three decimal places

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