Explanation The test hypotheses are given as follows: Denote p as the proportion of public preferring a product. Null hypothesis: H 0 : p ≥ 0.2 That is, the proportion of public preferring a product is 0.2. Alternative hypothesis: H a : p < 0.2 That is, the proportion of public preferring a product is 0.2, which is less than 0.2. Rejection region: In context, the level of the test, α , is 0.05. Here, the alternative is left-tailed test. Hence, the rejection region will be z < − z α . From the “Appendix 3, Table 4 Normal curve areas”, the critical value for the level of significance 0.05 is 1.645. Thus, the rejection region under level of significance of 0.05, is z < − 1.645 . Test statistic: The test statistic based on p ^ ( = Y n ) is given below: Z = p ^ − p 0 σ p ^ Where, p 0 is the hypothesized proportion, σ p ^ ( = p 0 ( 1 − p 0 ) n ) is the standard error of p ^ p ^ is the sample proportion, Y is the number of observations of interest, and n is the sample size

Mathematical Statistics with Applications

7th Edition

ISBN: 9780495110811

Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer

Publisher: Cengage Learning

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Chapter 10.3, Problem 30E

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Delineate how small would the sample percentage needed before the claim could be proved false.

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Chapter 10.3, Problem 29E

Chapter 10.3, Problem 31E

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ons 12. A sociologist hypothesizes that the crime rate is higher in areas with higher poverty rate and lower median income. She col- lects data on the crime rate (crimes per 100,000 residents), the poverty rate (in %), and the median income (in $1,000s) from 41 New England cities. A portion of the regression results is shown in the following table. Standard Coefficients error t stat p-value Intercept -301.62 549.71 -0.55 0.5864 Poverty 53.16 14.22 3.74 0.0006 Income 4.95 8.26 0.60 0.5526 a. b. Are the signs as expected on the slope coefficients? Predict the crime rate in an area with a poverty rate of 20% and a median income of $50,000. 3. Using data from 50 work

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Chapter 10 Solutions

Mathematical Statistics with Applications

Ch. 10.2 - Define and for a statistical test of hypotheses.Ch. 10.2 - An experimenter has prepared a drug dosage level...Ch. 10.2 - Refer to Exercise 10.2. a Find the rejection...Ch. 10.2 - Suppose that we wish to test the null hypothesis...Ch. 10.2 - Let Y1 and Y2 be independent and identically...Ch. 10.2 - We are interested in testing whether or not a coin...Ch. 10.2 - True or False Refer to Exercise 10.6. a The level...Ch. 10.2 - A two-stage clinical trial is planned for testing...Ch. 10.3 - A survey published in the American Journal of...Ch. 10.3 - The hourly wages in a particular industry are...

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