Homework: HW2 Instructions Please complete all problems. Unless otherwise noted, each problem is worth 5 points. To obtain full credit, you must use the methods specified in the course text. Please, format your work as explained in chapter 2 of the Frequently Asked Questions (FAQ) document. When doing calculations, such as the variance, standard deviation, or the correlation coefficient, use technology wherever possible. There is no need to do calculations by hand unless | direct you to do so. Rounding. You should round your z-scores to two decimal places when using a normal distribution table and the areas under the normal curve to decimal places. When using the t-distribution or doing other calculations, round to 3 decimal places unless otherwise directed. Never round until the last step of your calculations (Note: see FAQ 4.2). Testing claims. To avoid loss of points, you must meet all 5 requirements listed below whenever you are asked to test a claim or conduct a hypothesis test. Please carefully read the documents "Hypothesis Testing: Basics" and "Hypothesis Tests: Formatting Requirements" posted in the Files folder under Course Information. 1. State the null hypothesis, Ho, and the alternate hypothesis, Ha, indicating which is the claim. 2. Show the calculation of the test statistic. 3. Depending on the method you use, list either (a) the p-value or (b) find the critical value(s). Note: One tail tests have only one critical value, but two tail tests have two. 4. State decision whether to "reject" or "fail to reject" the null hypothesis, Ho- 5. State your conclusion about the claim. You should use the wording suggested by the author in the table in section 7.1. Assignment Problems Section 7.1 Problems 1 and 2 State whether the hypothesis test involves a left-tailed, right-tailed, or two-tailed test. 1. A researcher claims that at most 40% of Americans prefer coffee to tea. 2. A researcher claims that the average cost to rent a flat is less than $800 per month. 3. Write the statement of conclusion for this test. A researcher claims that the mean cost of a sedan is more than $36,000. For this research o = 0.05. Data is collected by the researcher and a hypothesis test is conducted. Based on the evidence, the decision is to reject the null hypothesis. Write the conclusion that the researcher should make with respect to the claim. Section 7.2 Problems 4-6 Complete the hypothesis test. Please remember to include all 5 parts of each hypothesis test mentioned in the instructions. 4. Test scores. For a random sample of 50 students, the mean test score was a = 76 points. Assume that o = 8 points and o = 0.01. A researcher claims that the population mean score is at most 75 points. Is there enough evidence to reject the researcher's claim? 5. Elapsed time. In a random sample of 60 technicians the mean time to repair an assembly was 14.8 minutes. Assume that o = 2.7 minutes and o = 0.05. A researcher claims that the population mean time for the repair is less than 15.5 minutes. Is there enough evidence to support the researcher's claim? 6. Weights. For a random sample of 55 students, the mean weight, a = 154.2 pounds. Assume that o = 6.9 pounds and o = 0.05. A researcher claims that the population mean weight is more than 152 pounds. Is there enough evidence to support the researcher's claim? Assume the population is normally distributed.Section 7.3 Problems 7-9 Complete the hypothesis test. Please remember to include all 5 parts of each hypothesis test mentioned in the instructions. 7. Test scores. In a random sample of 41 students, the mean test score was a = 78.1 points. Assume that s = 8.3 points and o = 0.025. A researcher claims that the population mean score is less than 80 points. Is there enough evidence to support the researcher's claim? 8. Text costs. For a random sample of 61 text book purchases the mean cost for a single book was a = $177.75. Assume that s = $15.90 and a = 0.05. A researcher claims that the population mean cost for a single text is less or equal to $175. Is there enough evidence to reject the researcher's claim? 9. Time in social media. In a random sample of 28 persons aged 30 to 45 the mean time spent per day using social media was, a = 93 minutes. Assume that s = 9 minutes and o = 0.01. A researcher claims that for persons aged 30 to 45, the population mean time using social media is different from 90 minutes. Is there enough evidence to support the researcher's claim? Assume the population is normally distributed. Section 7.4 Problems 10-12 Complete the hypothesis test. Please remember to include all 5 parts of each hypothesis test mentioned in the instructions. 10. Juice consumers. A researcher claims that less than 25% of juice consumers feel that grape flavor is their favorite. In a random sample of 148 juice consumers 30 said that grape was their favorite flavor. At a = 0.05 is there enough evidence to support the researcher's claim? 11. Computer preferences. A researcher claims that more than 35% of computer users prefer Apple computers. In a random sample of 225 adults 89 said that they preferred an Apple computer . At a = 0.05 is there enough evidence to support the researcher's claim? 12. Travel preferences. A researcher claims that the proportion of consumers who prefer traveling by air rather than by train is 75%. In a random sample of 182 consumers, 70% said that they preferred traveling by air rather by train. At a = 0.10, is there enough evidence to reject the researcher's claim? Section 7.5 Problems 13-15 Complete the hypothesis test. Please remember to include all 5 parts of each hypothesis test mentioned in the instructions. Assume the populations are normally distributed. 13. Claim: 2