A researcher selects a sample of 36 students from a school population with a mea

Question

A researcher selects a sample of 36 students from a school population with a mean IQ of 100 and standard deviation of 12. She determines that the mean IQ in this sample is 104. Assuming she computes a one-sample z test at a .05 level of significance for a two-tailed test what is the rejection region?

Answer each of the following questions:

What is the null hypothesis?

What is/are the critical values?

What is the standard error?

What is the test statistic?

Explain why you would retain or reject the null hypothesis? Provide the probability.

Would you calculate Cohen’s d? Why or why not?

Compute the value and the effect size of Cohen’s d

Explanation / Answer

Null hypothesis = H0 : mu = 104

Critical value for 0.05 = +/- 1.96

Standard error = s / sqrt(n) = 12 / sqrt(36) = 2

test statistic:

z = ( x - mean) / ( s /sqrt(n))
= ( 100 - 104) / ( 12/sqrt(36))
= -2

p value is calculated using z = -2
P value = 0.0455.

We reject the null hypothesis because p value is less than 0.05

No ,we can't calculate the cohen's d because Cohen’s d is simply a measure of the distance between two means, measured in standard deviations

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