Suppose a researcher wants to test whether the proportion of people that reflect a certain characteristic in a population, population A, is lower than the proportion of people with that characteristic in another population, population B. The researcher plans to perform a two-sample z‑test for two proportions, testing the null hypothesis,  ?0:?A−?B=0, against the alternative hypothesis, ?1:?A−?B<0, where ?A and ?B represent the proportions of people reflecting the characteristic of interest in population A and population B, respectively. The population size exceeds 5000 in population A and in population B. The researcher selects a simple random sample from each population and records the proportion of people in each sample that reflect the characteristic of interest. The sample results are summarized in the table. Population Sample size Sample proportion A ?A=44 ?̂A=0.6364 B ?B=70 ?̂B=0.7714 Given that the samples were randomly selected from large populations and the sample sizes are sufficiently large, the researcher can assume that the requirements for a two-sample z‑test for two proportions have been met. Compute the z‑statistic for this two-sample test of two proportions. Provide your answer precise to two decimal places. Avoid rounding until the final step.

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Suppose a researcher wants to test whether the proportion of people that reflect a certain characteristic in a population, population A, is lower than the proportion of people with that characteristic in another population, population B. The researcher plans to perform a two-sample z‑test for two proportions, testing the null hypothesis,  ?0:?A−?B=0, against the alternative hypothesis, ?1:?A−?B<0, where ?A and ?B represent the proportions of people reflecting the characteristic of interest in population A and population B, respectively.

The population size exceeds 5000 in population A and in population B. The researcher selects a simple random sample from each population and records the proportion of people in each sample that reflect the characteristic of interest. The sample results are summarized in the table.

Population Sample size Sample proportion
A ?A=44 ?̂A=0.6364
B ?B=70 ?̂B=0.7714

Given that the samples were randomly selected from large populations and the sample sizes are sufficiently large, the researcher can assume that the requirements for a two-sample z‑test for two proportions have been met.

Compute the z‑statistic for this two-sample test of two proportions. Provide your answer precise to two decimal places. Avoid rounding until the final step.

 

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