Suppose that the 101 randomly selected eighth-grade students (mentioned in question 6) took a “practice” test similar to the official standardized test a month before the official test was administered. The researchers reported that the (two-tailed) statistical test of the difference between the practice and official test scores resulted in t100 = -2.32, p < .05.(a) Given that the difference score was computed as D = (practice score – official score), do the reported results indicate that students scored significantly higher or lower on the official test relative to the practice test? Explain.(b) If we constructed the corresponding 95% confidence interval for the mean difference (between the practice and official test scores) in the population, would it include zero? Explain. 6. The State of Wisconsin is interested in the performance of its eighth-grade students on the standardizedeighth-grade mathematics assessment test. A research team, tasked by the State, obtains a random sampleof 101 eighth-grade student scores and finds that the sample mean is 265 and the sample standarddeviation is 55. The scores are approximately normally distributed.(a) Construct a 95% confidence interval for the mean test score in the population of Wisconsin eighth-graders and fully interpret your result.(b) The national average on this standardized eighth-grade mathematics assessment test is 260. Basedon the available data from Wisconsin (as described above), would you conclude that the averageperformance of Wisconsin students is significantly different from theperformance? Explain.averagenational

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Description: Suppose that the 101 randomly selected eighth-grade students (mentioned in question 6) took a “practice” test similar to the official standardized test a month before the official test was administered. The researchers reported that the (two-tailed)

From the provided information, The test statistic t = -2.32 And p < 0.05

Answered: Suppose that the 101 randomly selected…

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Suppose that the 101 randomly selected eighth-grade students (mentioned in question 6) took a “practice” test similar to the official standardized test a month before the official test was administered. The researchers reported that the (two-tailed) statistical test of the difference between the practice and official test scores resulted in t100 = -2.32, p < .05.

(a) Given that the difference score was computed as D = (practice score – official score), do the reported results indicate that students scored significantly higher or lower on the official test relative to the practice test? Explain.

(b) If we constructed the corresponding 95% confidence interval for the mean difference (between the practice and official test scores) in the population, would it include zero? Explain.

6. The State of Wisconsin is interested in the performance of its eighth-grade students on the standardized
eighth-grade mathematics assessment test. A research team, tasked by the State, obtains a random sample
of 101 eighth-grade student scores and finds that the sample mean is 265 and the sample standard
deviation is 55. The scores are approximately normally distributed.
(a) Construct a 95% confidence interval for the mean test score in the population of Wisconsin eighth-
graders and fully interpret your result.
(b) The national average on this standardized eighth-grade mathematics assessment test is 260. Based
on the available data from Wisconsin (as described above), would you conclude that the average
performance of Wisconsin students is significantly different from the
performance? Explain.
average
national

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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