A Consumer Reports Research Center survey of 427 women...

A Consumer Reports Research Center survey of 427 women showed that 29.0% of them purchase books online. a. Among the 427 women who were surveyed, what is the number of women who said that they purchase books online? b. Find a 95% confidence interval estimate of the percentage of all women who purchase books online. c. Can we safely conclude that less than 50% of all women purchase books online? Why or why not? d. Can we safely conclude that at least 25% of all women purchase books online? Why or why not? e. What do the results tell us about the percentage of men who purchase books online?

A Consumer Reports Research Center survey of 427 women showed that 29.0% of them purchase books online.
a. Among the 427 women who were surveyed, what is the number of women who said that they purchase books online?
b. Find a 95% confidence interval estimate of the percentage of all women who purchase books online.
c. Can we safely conclude that less than 50% of all women purchase books online? Why or why not?
d. Can we safely conclude that at least 25% of all women purchase books online? Why or why not?
e. What do the results tell us about the percentage of men who purchase books online?

Key Concepts

Sample Proportion

This concept refers to the ratio of individuals in a sample who exhibit a particular characteristic compared to the total number in the sample. In the given problem, 29.0% represents the sample proportion of women who purchase books online, which is used as an estimate of the population proportion.

Confidence Interval Estimation

A confidence interval for a proportion is a range of values, derived from the sample data, that is likely to contain the true population proportion. In practice, a 95% confidence interval means that if many samples were taken, approximately 95% of such calculated intervals would contain the actual population percentage of women who purchase books online.

Margin of Error

Margin of error is the amount added and subtracted from the sample statistic to create the confidence interval. It reflects the uncertainty associated with sampling and can be calculated based on the standard error of the sample proportion, typically using the normal approximation for large samples.

Statistical Inference

Statistical inference involves drawing conclusions about a population based on sample data. In this case, one can infer about whether the population proportion exceeds or falls below certain thresholds (like 50% or 25%) by examining the confidence interval and determining if those values lie within it or not.

Generalization and External Validity

This concept addresses the extent to which the results obtained from a sample can be applied to the broader population or to other groups. In the problem, since the data were collected only from women, the results cannot be directly generalized to men or other populations without appropriate supporting data.

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