Based on the sample results in Exercise 10.69, construct and interpret the 95% confidence interval for the population proportion. Is the hypothesized proportion (0.55) within the interval? Given the presence or absence of the 0.55 value within the interval, is this consistent with the findings of the hypothesis test conducted in Exercise 10.69?
In exercise
According to the National Association of Home Builders, 55% of new single-family homes built during 2005 had a fireplace. Suppose a nation wide homebuilder has claimed that its homes are “a cross section of America,” but a simple random sample of 600 of its single-family homes built during that year included only 50.0% that had a fireplace. Using the 0.05 level of significance in a two-tail test, examine whether the percentage of sample homes having a fireplace could have differed from 55% simply by chance. Determine and interpret the p-value for the test.