Question

A teacher claims 9 year old girls are taller than 9 year old boys. Test this claim at an alpha level of .05. A researcher randomly selected a smaple of 60 boys and sample of 50 girls.  

Boys: n=60 mean = 123.5 cm standard deviation = 9.9 cm

Girls: n=50 mean = 126.2 cm standard deviation = 10.9 cm

Use either one sample t or z test. Label critical value and test value. State p value and show all five steps of analysis.

Answer 1

Answer)

Null hypothesis Ho : u 1 = u 2

Alternate hypothesis Ha : u 1 < u 2

Where u 1 is for boys and u 2 is for girls

As the population s.d is unknown and we are given with sample s.d, we will use t test

Test statistics z = (u1-u2)/standard error

Standard error = √{(s1^2/n1)+(s2^2/n2)}

u1 = 123.5, u2 = 126.2

N1 = 60, N2 = 50

S1 = 9.8, S2 = 10.9

Test statistics t = -1.348

Degrees of freedom is = smaller of n1-1, n2-1

Df = 49

For df 49 and alpha 0.05, critical value from t distribution is = -1.677

And P-Value for -1.348 test statistics is = 0.0919

As the obtained P-Value is greater than 0.05(given significance level)

We fail to reject the null hypothesis

And we do not have enough evidence to support the claim