Text: About 40% of homeowners in California should have earthquake insurance. A public official is concerned that too few homeowners are buying insurance. In a survey of 337 randomly selected homes, 133 are found to be insured. Name the parameter the public official is concerned about? Null and alternative hypothesis? Z and p-value?
Correction: About 40% of homeowners in California should have earthquake insurance. A public official is concerned that too few homeowners are buying insurance. In a survey of 337 randomly selected homes, 133 are found to be insured.
Parameter the public official is concerned about: The proportion of homeowners in California who have earthquake insurance.
Null hypothesis: The proportion of homeowners in California who have earthquake insurance is equal to 40%.
Alternative hypothesis: The proportion of homeowners in California who have earthquake insurance is less than 40%.
Z-value: To calculate the Z-value, we need the sample proportion, the population proportion, and the sample size. The Z-value can be calculated using the formula: Z = (sample proportion - population proportion) / sqrt((population proportion * (1 - population proportion)) / sample size)
P-value: The p-value is the probability of obtaining a test statistic as extreme as the observed result, assuming the null hypothesis is true. It can be calculated using a Z-table or statistical software.