Question

Mathew is interested in the relationship between a learning game Power Physics and Creativity. He has developed an instrument for testing Creativity. After some initial pilot tests, he and Russell work out that the hypothesized mean creativity score should be 7 and the standard deviation for creativity scores should be around ? = 2.3. Standard error = 0.5019

Mathew is pleased to see a positive difference in the pilot sample, but Russell is cautious about committing a Type I error. What is the Type I error, and what is its probability of occurrence?

Answer 1

solution ) according to question null and alternate hypotheses are :

H0 : hypothised meean is equal to 7 , = 7 ;

H1 : 7 ,

so , type I error , is the probability of rejecting the null hypothesis when null hypothesis is true .

which means , we are rejecting =7 and accepting 7 , either less than 7 or greater than 7 .

And , probability of type I error is symbolized or denoted by alpha () , which is the level of significance .

and from standard error formula , S.E = / sqrt (n)

n = 21 .

if , we let x = 8 (say)

then z score = {(x - ) *sqrt(n) } /

= {(8-7) * sqrt(21) } / 2.3 = 1.99

so now , alpha level corresponding to z score of 1.99 is 5 percent or near about 5 % chance is of committing type I error .

I HOPE I WAS HELPFUL AND HAVE CLEARED YOUR DOUBTS.

THANKYOU