Answered: (i) Test the claim that p is less than…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 10CYU

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disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 223 numerical entries from the file and r = 48 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1.

(i) Test the claim that p is less than 0.301. Use ? = 0.05.

(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: p < 0.301; H₁: p = 0.301H₀: p = 0.301; H₁: p > 0.301 H₀: p = 0.301; H₁: p < 0.301H₀: p = 0.301; H₁: p ≠ 0.301

(b) What sampling distribution will you use?

The standard normal, since np > 5 and nq > 5.

The standard normal, since np < 5 and nq < 5.

The Student's t, since np < 5 and nq < 5.

The Student's t, since np > 5 and nq > 5.

What is the value of the sample test statistic? (Round your answer to two decimal places.)

(c) Find the P-value of the test statistic. (Round your answer to four decimal places.)

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