Answer:
We conclude that the new teaching method does not negatively affects reading comprehension scores.
Step-by-step explanation:
We are given that an educational psychologist wants to test whether a new teaching method negatively affects reading comprehension scores.
She randomly selects 30 6th grade students that were taught under the new teaching method and finds that their scores on a standardized reading comprehension test have a mean equal to 118.8 with a variance equal to 37.2.
Scores on the standardized test in the general population of 6th graders are distributed approximately normally with a mean equal to 119.8.
<em>Let </em><em> = mean scores on a standardized reading comprehension test.</em>
So, Null Hypothesis, : 119.8 {means that the new teaching method does not negatively affects reading comprehension scores}
Alternate Hypothesis, : < 119.8 {means that the new teaching method negatively affects reading comprehension scores}
The test statistics that would be used here <u>One-sample t test statistics</u> as we don't know about the population standard deviation;
T.S. = ~
where, = sample mean test score = 118.8
s = sample standard deviation = = 6.1
n = sample of 6th grade students = 30
So, <u><em>test statistics</em></u> = ~
= -0.898
The value of t test statistics is -0.898.
Since, in the question we are not given with the level of significance so we assume it to be 5%. <u>Now, at 5% significance level the t table gives critical value of -1.699 for left-tailed test.</u>
Since our test statistic is more than the critical value of t as -0.898 > -1.699, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u>we fail to reject our null hypothesis</u>.
Therefore, we conclude that the new teaching method does not negatively affects reading comprehension scores.