please solve all parts, i want the answers as a word file. Suppose that the mean

Question

please solve all parts, i want the answers as a word file.

Suppose that the mean on an L.Q. test is known to be 100 for the general population. We are interested in whether a particular group of children in a kindergarten class score significantly higher or lower than the typical mean I.Q. score. We obtain a sample of the 20 children, administer the l.Q. test to them, and get the following results: M: 103 and ? 10. a. b. ?. d. not? e. What are the null and alternative hypotheses for this situation? What is the estimated standard error of the mean? Perform the appropriate statistical test, with a .05. Describe the results of your findings. Is this test statistically significant? Why or why Compute the 95% confidence interval. Compute the effect size.

Explanation / Answer

Answer

Part (a)

Null Hypothesis (Ho): µ = 100

Alternative Hypothesis (Ha): µ =/ 100

Part (b)

SE = sigma / sqrt (n) = 10/sqrt(20) = 2.2361

The estimated standard error of the mean is 2.2361

Part (c)

z = ( x bar – Mean ) / SE

= (103-100)/ 2.2361

= 1.34

Part (d)

The critical z at 5% level of significance from normal table we get as (-/+) 1.96.

Here 1.34 falls in between the critical values (-1.96 and 1.96). We fail to reject the null hypothesis.

There is not sufficient evidence to conclude that a kindergarten class score significantly higher or lower than the typical mean I.Q. score.

Part ( e)

Confidence Interval:

X bar (-/+) E

X bar = 103

E = zc * ( sigma / sqrt (n)) = 1.96 * (10/sqrt(20)) = 4.38

X bar (-/+) E

103 (-/+ ) 4.38

98.62 and 107.38

The 95% confidence interval is equal to (98.62 and 107.38)

Part (f)

Effect size = (103-100)/10 = 0.3

Hence;

The value of the effect size is equal to 0.3

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