Find the requested value. A researcher for a car insurance company wishes to estimate the mean annual premium that men aged 20-24 pay for their car insurance. A random sample of 16 men aged between 20 and 24 yields the following annual premiums, in dollars. 763 607 679 578 856 503 578 554 820 967 576 715 857 607 711 986 Use the data to obtain a point estimate of the mean annual premium for all men aged between 20 and 24. Round your answer to the nearest dollar. $693 $710 $689 $701
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Lucas F.
Parents of teenage boys often complain that auto insurance costs more, on average, for teenage boys than for teenage girls. A group of concerned parents examines a random sample of insurance bills. The mean annual cost for 36 teenage boys was $679. For 23 teenage girls, it was $559. From past years, it is known that the population standard deviation for each group is $180. Determine whether or not you believe that the mean cost for auto insurance for teenage boys is greater than that for teenage girls.
Hypothesis Testing with Two Samples
Two Population Means with Known Standard Deviations
Allstate Insurance is one of the major automobile insurance companies in the country. Recently, the western region claims manager instructed an intern in her department to test if there exists any difference between the mean years that male customers have been insured by Allstate versus female customers. The intern randomly selected 13 male and 13 female customers from the account records and the summary is given below (rounded to the nearest year). Sample Mean - Male = 12, Sample Variance - Male = 3 Sample Mean - Female = 7, Sample Variance - Female = 4 a. Does this data suggest that there exists a difference in the average years insured by All State between male and female? Use α = 0.05. b. Find the p-value for the test. Please provide Hypothesis, Test Statistic, and Rejection Region Graph.
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