Math 170: Elementary Statistics for Social Science



Math 170: Elementary Statistics for Social Science

Hypothesis Test for Means – Homework Problems

Example 1: A machine is designed to fill jars with 16 ounces of coffee. A consumer suspects that the machine is not filling the jars completely. A sample of 8 jars has a mean of 15.6 ounces and a standard deviation of 0.3 ounce. Is there enough evidence to support the consumer’s conjecture at [pic]? Yes. T=-3.77, p-value= .007

Example 2: In order to monitor the ecological health of the Florida Everglades, various measurements are recorded at different times. The bottom temperatures are recorded at the Garfield Bight station and the mean of 30.4 C is obtained for 61 temperatures recorded on 61 different days. Assuming that the population standard deviation is 1.7 C, test the claim that the population mean is 30 C. Use a 0.05 significance level. No. z=1.84 p-value= .066

Example 3: The health of the bear population in Yellowstone National Park is monitored by periodic measurements taken from anesthetized bears. A sample of 54 bears has a mean weight of 182.9 lb. Assuming the population standard deviation is known to be 121.8. Use a 0.10 significance level to test the claim that the population mean of all such bear weights is 200 lb. No. z=-1.03, p-value=.30

Example 4: A job placement director claims that the average starting salary for nurses is $24,000. A sample of 10 nurses has a mean of $23,450 and a standard deviation of $400. Is there enough evidence to reject the director’s claim at [pic]? Yes. t=-4.35, p-value = .002

Example 5: A physician claims that joggers’ maximal volume oxygen uptake is about the same as the average of all adults. A sample of 15 joggers has a mean of 43.6 milliliters per kilogram (ml/kg) and a standard deviation of 6 ml/kg. If the average of all adults is 36.7 ml/kg, is there enough evidence to support the physician’s claim at [pic]? Yes. t=4.45, p-value=.001.

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