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MAT 160 ? Hypothesis Testing Homework




Question;MAT 160 ? Hypothesis Testing HomeworkName _______________________1.) Employees in an accounting firm claim that the mean salary of the firm?s accountants is less than that of its competitor?s which is $45,000. (Assume that the standard deviation of the firm?s accountants is known to be $5,200.) A random sample of 30 of the firm?s accountants has a mean salary of $43,500. Test the employees claim at the.01 level of significance.1.2. 3. 4. 5.2.) The U.S. Department of Agriculture reports that the mean cost of raising a child from birth to age 2 in a rural area is $8390. You believe this value is incorrect, so you select a random sample of 900 children (age 2) and find that the mean cost is $8275. Assume the standard deviation for the cost of raising a child from birth to age 2 is $1540. Test your claim at the.05 level of significance. 1.2. 3. 4. 5.3.) You receive a brochure from a large university. The brochure indicates that the mean class size for full-time faculty is less than 32. You want to test this claim. You randomly select 18 classes taught by full-time faculty and determine the class size of each. The results are listed below. Can you support the university?s claim at the.01 level of significance? Assume class size is known to be normally distributed.30 30 31 32 33 33 34 32 29 25 20 33 33 33 31 32 30 341.2. 3. 4. 5.4.) A company that makes cola drinks states that the mean caffeine content per one 12-ounce bottle of cola is 40 milligrams. Suppose you work as a quality control manager and are asked to verify this claim. During your tests, you find that a random sample of thirty 12-ouce bottles of cola has a mean caffeine content of 39.2 milligrams and a standard deviation of 1.59. Assume caffeine content is normally distributed. Can you reject the claim at the.01 level of significance? 5.) In 1998, the Department of Agriculture estimated that a typical U.S. family of four would spend $157 per week for food. A random sample of 8 Kansas families of four that year yielded the following weekly food costs:143169149135138152150141Does the data provide sufficient evidence at the.10 level of significance to conclude that in 1998 the mean weekly food cost for Kansas families of four was less than the national mean of $157? Suppose it is known that the population is not normally distributed, but it is a safe assumption that the population is symmetric.1.2. 3. 4. 5.Worksheet guide linesThe five steps to a hypothesis test:1. State your null and alternate hypotheses.2. State your level of significance (alpha).3. State the test you are using and the p-value.4. Compare your p-value to alpha and make your decision.5. State your conclusion as a sentence


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