Question

A researcher knows that scores on a standardized language measure are normally distributed with a μ = 50 and σ = 20. She wants to know if an online computer program will improve scores on the standardized test. She gives a sample of n = 25 students the study program and calculates the sample mean (M = 60) for her group of students that received the study program. She calculates her test statistic to be z = 2.5 ! She give the test to another group of students. If the children completing the online computer program in this group scored a M = 55, what would their test statistic z be equal to (as noted above μ = 50 and σ = 20 )? Would you reject or accept this null hypothesis for this new group of students (using a two tail test, α = .05) What would a type I error be in the context of this example?

I need help with the all three parts

Answer 1

For new group we have

Sample size=n=25

We already know that SD=SD=20

Sample mean=M=55

As mentioned we need to test that if new group mean score is equal to 50 or not hence

1.

Test statistics is given by

2.

Since test is two tailed so

Pvalue =2*P(Z>1.25)=2*0.106=0.212

Since P value is more than level of significance(0.05) hence we failed to reject H0

So we accept the null hypothesis.

3.

Since Type 1 error is defined as falsely rejecting H0 so in our case

Type 1 error is we have concluded that mean score is different from 50 but in actual mean score is 50.

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