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According to a survey in 2019, about 31% (0.31) of American households still had a landline. However, Jack feels the statistic is outdated, and the actual proportion would be less than the proposed one. So, he does his own survey of 150 households randomly, and 37 of them have a landline. Test whether Jack's conjecture is statistically valid under a 0.05 significance level. (For this question, please refer to pages 31 and 36 in the Statistics Review slide.) (i) State null and alternative hypotheses. You can use plain language for those, e.g., "The null hypothesis is that ..." / "The alternative hypothesis is that ...". (ii) Suppose x is the number of households with a landline and n is the surveyed households. Calculate the sample proportion p with x and n, and save it in a variable p.hat. In addition, find po value based on the problem description, and save it in p.null. (iii) Compute the Z-test statistic and p-value based on the p.null and p.hat. (iv) Compare your result with the R procedure prop.test() with argument correct=FALSE. (v) Make a conclusion under the given significance level whether or not you would reject the null hypothesis to follow the alternative hypothesis.

According to a survey in 2019, about 31% (0.31) of American households still had a landline. However, Jack feels the statistic is outdated, and the actual proportion would be less than the proposed one. So, he does his own survey of 150 households randomly, and 37 of them have a landline. Test whether Jack's conjecture is statistically valid under a 0.05 significance level. (For this question, please refer to pages 31 and 36 in the Statistics Review slide.) (i) State null and alternative hypotheses. You can use plain language for those, e.g., "The null hypothesis is that ..." / "The alternative hypothesis is that ...". (ii) Suppose x is the number of households with a landline and n is the surveyed households. Calculate the sample proportion p with x and n, and save it in a variable p.hat. In addition, find po value based on the problem description, and save it in p.null. (iii) Compute the Z-test statistic and p-value based on the p.null and p.hat. (iv) Compare your result with the R procedure prop.test() with argument correct=FALSE. (v) Make a conclusion under the given significance level whether or not you would reject the null hypothesis to follow the alternative hypothesis.

Operations Research : Applications and Algorithms
Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter16: Probabilistic Inventory Models
Section16.4: The News Vendor Problem: Continuous Demand
Problem 1P
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According to a survey in 2019, about 31% (0.31) of American households still had a landline. However, Jack feels the statistic is outdated, and the actual proportion would be less than the proposed one. So, he does his own survey of 150 households randomly, and 37 of them have a landline. Test whether Jack's conjecture is statistically valid under a 0.05 significance level. (For this question, please refer to pages 31 and 36 in the Statistics Review slide.) (i) State null and alternative hypotheses. You can use plain language for those, e.g., "The null hypothesis is that ..." / "The alternative hypothesis is that ...". (ii) Suppose x is the number of households with a landline and n is the surveyed households. Calculate the sample proportion p with x and n, and save it in a variable p.hat. In addition, find po value based on the problem description, and save it in p.null. (iii) Compute the Z-test statistic and p-value based on the p.null and p.hat. (iv) Compare your result with the R procedure prop.test() with argument correct=FALSE. (v) Make a conclusion under the given significance level whether or not you would reject the null hypothesis to follow the alternative hypothesis.
Transcribed Image Text:According to a survey in 2019, about 31% (0.31) of American households still had a landline. However, Jack feels the statistic is outdated, and the actual proportion would be less than the proposed one. So, he does his own survey of 150 households randomly, and 37 of them have a landline. Test whether Jack's conjecture is statistically valid under a 0.05 significance level. (For this question, please refer to pages 31 and 36 in the Statistics Review slide.) (i) State null and alternative hypotheses. You can use plain language for those, e.g., "The null hypothesis is that ..." / "The alternative hypothesis is that ...". (ii) Suppose x is the number of households with a landline and n is the surveyed households. Calculate the sample proportion p with x and n, and save it in a variable p.hat. In addition, find po value based on the problem description, and save it in p.null. (iii) Compute the Z-test statistic and p-value based on the p.null and p.hat. (iv) Compare your result with the R procedure prop.test() with argument correct=FALSE. (v) Make a conclusion under the given significance level whether or not you would reject the null hypothesis to follow the alternative hypothesis.
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