Assume that a simple random sample has been selected from a normally distributed

Question

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative hypotheses, test statistic critical value(s), and state the final conclusion that addresses the original claim. A simple random sample of pages from a dictionary is obtained. Listed below are the numbers of words defined on those pages Given that this dictionary has 1459 pages with defined words the claim that there are more than 70,000 defined words is the same as the claim that the mean number of defined words on a page is greater than 48.0. Use a 0.01 level significance level to test this claim. What does the result suggest about the claim that there are more than 70.000 defined words in the dictionary? 44 36 64 67 40 64 38 34 74 79 What are the null and alternative hypotheses? A. J_0: mu = 48.0 H_1: mu > 48.0 B. H_0: mu = 48.0 H_ 1: mu 48.0 H_1: mu = 48.0 Identity the test statistic

Explanation / Answer

H0: mu = 48 against h1: mu> 48

Mean (Xbar) of given values is 54

n= 10

Find (x-xbar)^2 for each value then take addition of these values.

s = sum(x-xbar)^2

test statistic value is less that critical value hence there is no evidence to reject null hypothesis.

X (x-xbar)^2 44 1936 36 1296 64 4096 67 4489 40 1600 64 4096 38 1444 34 1156 74 5476 79 6241 Total 31830 Mean 54 s^2 3183 s 56.41808 s/sqrt(n) 17.84096 Test statistic -1.70563 Critical value -1.83311

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