Name: ______One Sample Inference Mixed Review Activity

Statistics

State the Inference for each problem, document the hypothesis statement if necessary, find the answer and write a proper conclusion

  1. Based on information from State Farm Insurance Company, 67% of all damage liability claims are made by single people under the age of 25. A random sample of 53 claims in CollinCounty showed 42 claims were made by single people under the age of 25. Does this indicate that the percent of insurance claims by single people under the age of 25 in CollinCounty is higher than the national percent?
  1. A forester wishes to estimate the mean growth of seedlings in a large timber plot since last year. A random sample of 100 seedlings is taken and it is found that the one-year growth yields an average of 12.8 cm and a standard deviation of 2.5 cm. Give a 95% confidence interval for the mean growth.
  1. The average hemoglobin count (HC) for healthy adult women is 14 grams per 100 milliliters of whole blood. Suppose that a female patient has taken 12 laboratory blood samples during the past year. The HC counts sent to her doctor are listed below. Does the information indicate that this patient has significantly higher HC than the population?

191423201519211618181621

  1. In a random sample of 250 high school students, it was found that 84% of them later graduated. Find the 98% confidence interval for the true proportion of all high school students who graduate.
  1. The following information is taken from the U.S. Department of Commerce Environmental Data Service. Below is the average temperature (in Fahrenheit) for Buffalo, New York and Grand Rapids, Michigan. Do these data indicate that there is a difference in average temperatures?

MonthJFMAMJJASOND

Buffalo25.124.532.343.354.664.770.368.962.651.840.029.5

Gr. Rapids24.424.433.946.557.968.072.670.663.252.139.328.5

  1. For their total production of light bulbs, the management of an electronics firm knows that σ = 150 hours. How large a sample is needed if they want to be 90% confident that the estimate of the average production time will be within 30 hours of the correct value?
  1. According to government data, 22% of American children under the age of 6 live in households with incomes less than the official poverty level. A study of learning in early childhood chooses an SRS of 300 children.

a)What is the probability that less than 20% of the sample are from poverty households? (Remember to check that you can use the normal approximation.)

b)What is the probability that more than 25% of the sample is from poverty households?