Topic: Hypothesis test for the population mean: Z test On a standard anagram task (anagrams are sets of scrambled letters that must be arranged to form words), people successfully complete a mean, μ , of 25 anagrams. The standard deviation of this number is 6 anagrams. A researcher claims that the arousal from anxiety is distracting and will decrease task performance and, hence, decrease the mean number of anagrams completed. A random sample of 50 anxiety-ridden subjects was tested on the task, and the mean number of anagrams solved was 23. Can we support the researcher's claim at the 0.05 level of significance? (Assume no change in the population standard deviation among anxiety-ridden subjects.) Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) I know H0: (mean) = 25 & H1: (mean) < 25 & that I use a Z-test - Find the value of the test statistic. (Round to three or more decimal places. - Find the critical value. (Round to three or more decimal places.) - Can we support the researcher's claim that the arousal from anxiety will decrease the mean number of anagrams completed?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Topic: Hypothesis test for the population mean: Z test

On a standard anagram task (anagrams are sets of scrambled letters that must be arranged to form words), people successfully complete a mean, μ , of 25 anagrams. The standard deviation of this number is 6 anagrams. A researcher claims that the arousal from anxiety is distracting and will decrease task performance and, hence, decrease the mean number of anagrams completed. A random sample of 50 anxiety-ridden subjects was tested on the task, and the mean number of anagrams solved was 23. Can we support the researcher's claim at the 0.05 level of significance? (Assume no change in the population standard deviation among anxiety-ridden subjects.)

Perform a one-tailed test. Then complete the parts below.

Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.)

I know H0: (mean) = 25

& H1: (mean) < 25

& that I use a Z-test

- Find the value of the test statistic. (Round to three or more decimal places.

- Find the critical value. (Round to three or more decimal places.)

- Can we support the researcher's claim that the arousal from anxiety will decrease the mean number of anagrams completed?

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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