The local school board has instituted a book rewards program intended to encourage third graders to

rose2904ks

rose2904ks

Answered question

2022-06-18

The local school board has instituted a book rewards program intended to encourage third graders to read more, thereby increasing their scores on a standardized vocabulary test. Nationally, the average score on this exam among third graders is 98. A random sample of 223 local third graders participating in the program scored an average of 104 on the test with a standard deviation of 13.
Conduct a significance test with a=.05 to answer the research question: Is the program working to significantly increase local third graders' vocabulary scores?
STEP ONE
In step one of this significance test, do you have to have a "random sample" or "independent random samples"?
a) a random sample
b) independent random samples

Answer & Explanation

nuvolor8

nuvolor8

Beginner2022-06-19Added 32 answers

Given Information:
The average score on this exam among third graders is 98. i.e., μ0=98
Sample size n=223
Sample mean x ¯ =104
Standard deviation s=13
Significance level α=0.05
In step one of this significance test, do you have to have a "random sample" or "independent random samples":
It is a random sample (given)
State the hypothesis as follows:
Null Hypothesis H 0 : μ = 98  or  H 0 : μ 98 Alternative Hypothesis H 1 : μ > 98
Calculation of the test statistic:
t = x ¯ μ 0 8 n = 104 98 13 223 = 6 0.8705443892 = 6.892239011 6.892
Thus, the value of the test statistic is 6.892
Degrees of freedom df=223-1=222Using technology, critical value for a right tailed test at 222 degrees of freedom and 0.05 significance level is 1.6517
Since, computed value of the test statistic is greater than the critical value, Reject the null hypothesis.
Therefore, there is sufficient evidence to conclude that the average score on this exam among local third graders is greater than 98.
Thus, we can conclude that the program is working to significantly increase local third graders' vocabulary scores.

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