#3 and #4 What effect does increasing sample size have on power, beta, and alpha

Question

#3 and #4 What effect does increasing sample size have on power, beta, and alpha? For each, state why. Suppose that children in the first grade of a particular city's school system average 52 points on a standardized reading test. A psychologist is interested in testing the theory that economic deprivation leads to learning difficulties in children. One school in the system is located in an economically deprived area The average score of the 41 first-graders in this school is 46 points, with a standard deviation of 21. Is this information consistent with the theory? Perform the appropriate statistical test, listing the assumptions, hypotheses, computations, observed and critical values (use an alpha of 0.05), decisions and conclusions. A group of 25 tenth-graders were placed into a gifted class based on their previous classroom performance. The school psychologist gave this group of students an IQ test to determine whether they score significantly higher than average. It is known that for this particular IQ test, the mean of the population is 100 and the standard deviation is 16. The psychologist found the gifted students to have an average IQ of 105. Did they score significantly above the normal average? Perform the appropriate statistical test, listing the assumptions, hypotheses, computations, observed and critical an alpha of .05), decisions, and conclusions. We are interested in determining the number of m & ms that an average 10 year-old can stuff in its mouth before choking. We take 16 ten-year-olds, and measure the number of m & ms that each can stuff in its mouth. The mean of the 16 kids is 50 and the standard deviation is 10. Determine the 95% and 99% confidence intervals for the true mean number of m & ms for the population of 10 year-olds. Describe the confidence intervals in words.

Explanation / Answer

question 2

Hypothesis is

H0 : Economic depriviation does not lead to learning difficulties in children , mean = 52

H1 : Economic depriviation leads to learning difficulties in children , Mean < 52

now the T stat is calculated as

T = (Population mean - sample mean) / (sd/sqrt(N))

, where N = 41, SD = 21 and Sample mean = 46

so t stat is (52-46)/(21/sqrt(41)) = 1.82

Now we check the t critical value for n-1 degrees of freedom , which is 41-1 = 40 and alpha = 0.05 for 1 tail test as this is a directional test , which is 1.68

now as the t stat > t critical , hence we reject the null hypothesis in favor of alternate hypothesis and conclude that Economic depriviation leads to learning difficulties in children .

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