A science teacher claims that the mean scores on a science assessment test for f

Question

A science teacher claims that the mean scores on a science assessment test for fourth grade boys and girls are equal. The mean score for 13 randomly selected boys is 151 with a standard deviation of 36, and then mean score for 15 randomly selected girls is 149 with a standard deviation of 34. At = 0.01, can you reject the teacher’s claim? Assume the population are normally distributed and the population variances are equal.

Find the appropriate standardized test statistic and the P- value.

What can you say about the results?

Explanation / Answer

Solution:

Null Hypothesis (Ho): µ1 = µ2

Alternative Hypothesis (Ha): µ1 µ2

Pooled standard deviation, Sp = [(n1-1)s1^2+(n2-1)s2^2]/(n1+n2-2)

Pooled standard deviation, Sp = [(13-1)(36)^2+(15-1)(34)^2]/(13+15-2)

Pooled standard deviation, Sp = 1220.615

Pooled standard deviation, Sp = 34.937

Test statistics

t = (X-bar1 – X-bar2)/Sp 1/n1 + 1/n2

t = (151 – 149)/34.937 1/13 + 1/15

t = 0.15

Degrees of freedom, df = n1 + n2 – 2 = 13 + 15-2 = 26

Using t-tables, the p-value is

P [t (26) 0.15] = 0.8819

Since p-value is greater than 0.01 significance level, we fail to reject Ho.

Hence, we cannot reject the teacher’s claim.   

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.