Download Statistics Exam 3: Hypothesis Testing and Descriptive Statistics and more Exams Mathematics in PDF only on Docsity! Statistics 150: Introduction to Statistics I (Sec. 1) Exam 3 - Ch. 8, 9.1, 9.2 Winter 2002 Name: Directions: This exam contains six problems worth a total of 100 points. For each computa- tional problem, you must first write the formula to be used and present all your subsequent work in order to receive full or partial credit. 1. The manufacturer’s suggested retail price (MSRP) of certain computer software is $399. The actual retail prices of this software were obtained from randomly selected 35 stores, yielding a mean price of $387 with a standard deviation of $7. Test the hypothesis that the mean retail price of this software at all retail stores is lower than MSRP using the significance level of .01. (15 pts.) H0 : vs. H1 : Show the supporting work. State the decision (reject or retain H0) and interpret the result in the context of the problem. 2. Statisticians believe that many commercially produced dice are biased. In particular, they suspect that the side for 1 is heavier (because there is only one hole) and that the side for 6 is lighter (because there are six holes). A statistician purchased a typical die and rolled it 600 times. As a result, she observed 6 for 119 times. Perform a test to de- termine whether her die is more likely than expected to show 6. Use α = .01. (15 pts.) H0 : vs. H1 : Compute the test statistic and find the p-value. Based on the p-value obtained above, make the decision (reject or retain H0) and interpret the result in the context of the problem. 1 3. The question “Should the state government provide more financial support to students attending a private college?” was anchored with the responses 1 = “definitely no” to 7 = “definitely yes.” The participants of the survey were random samples of 40 stu- dents attending a private college and 50 students attending a public university. The summary of the results is shown below. Test whether students attending private col- leges and those attending public universities have different opinions on the issue. Use α = .01. (15 pts.) School x̄ s n Private (1) 5.2 0.6 40 Public (2) 4.7 1.1 50 H0 : vs. H1 : Show the supporting work. State the decision (reject or retain H0) and interpret the result in the context of the problem. 4. Based on a random sample of n = 24, the mean diameter of the trunk of a particular type of 50-year-old coniferous tree was found to be 35 inches with a standard deviation of 4 inches. (a) With an alpha level of .05, test the truth of the conjecture that the mean diam- eter of the trunk of this type of tree is 33 inches. (15 pts.) H0 : vs. H1 : Show the supporting work. State the decision (reject or retain H0) and interpret the result in the context of the problem. (b) Find the approximate observed significance level (p-value) of the test conducted in Part (a). (5 pts.) 2
