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Sample:2

Students require different amounts of sleep. A sample of 59 students at a large midwest university reported the following hours of sleep the previous night.

elizabethhayes
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Sample:2

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  1. Students require different amounts of sleep. A sample of 59 students at a large midwest university reported the following hours of sleep the previous night.

  2. One company, actively pursuing the making of green gasoline, starts with biomass in the form of sucrose and converts it into gasoline using catalytic reactions. At one step in a pilot plant process, the output includes carbon chains of length 3. Fifteen runs with same catalyst produced the product volumes (liter) While mean product volume is the prime parameter, it is also important to control variation. Conduct a test with the intent of showing that the population standard deviation σ is less than .8 liter. Use α=0.05

  3. A brochure inviting subscriptions for a new diet program states that the participants are expected to lose over 22 pounds in five weeks. Suppose that, from the data of the five-week weight losses of 56 participants, the sample mean and standard deviation are found to be 23.5 and 10.2 pounds, respectively. Could the statement in the brochure be substantiated on the basis of these findings? Test with α=0.05. Also calculate the P-value and interpret the result.

  4. The petal width (mm) of one kind of iris has a normal distribution. Suppose that, from a random sample of widths, the @uni:href based 90% confidence interval for the population mean width is (16.8, 19.6) mm. Answer each question “yes,” “no,” or “can't tell,” and justify your answer. On the basis of the same sample: (a) Would H0 : µ= 20 be rejected in favor of H0 : µ≠ 20 at α = 0.10 ? (b) Would H0 : µ= 18 be rejected in favor of H0 : µ≠ 18 at α = 0.10 ? (c) Would H0 : µ= 17 be rejected in favor of H0 : µ≠ 17 at α = 0.05? (d) Would H0 : µ= 22 be rejected in favor of H0 : µ≠ 22 at α = 0.01?

  5. One semester, an instructor taught the same computer course at two universities located in different cities. He was able to give the same final at both locations. The student's scores provided the summary statistics. Sample:1 Sample:2

  6. Rural and urban students are to be compared on the basis of their scores on a nationwide musical aptitude test. Two random samples of sizes 90 and 100 are selected from rural and urban seventh-grade students. The summary statistics from the test scores are Urban Rural Construct a 98% confidence interval for the difference in population mean scores between urban and rural students.

  7. Psychologists have made extensive studies on the relationship between child abuse and later criminal behavior. Consider a study that consisted of the follow-ups of 52 boys who were abused in their preschool years and 67 boys who were not abused. The data of the number of criminal offenses of those boys in their teens yielded the following summary statistics. Notabused Abused Construct a 98% confidence interval for the difference in population mean scores between urban and rural students.

  8. Do these data demonstrate that the proportion of persons who have ≤ 8 hours of sleep per night is significantly higher for the age group 30 to 40 than that for the age group 60 to 70? Answer by calculating the p-value.

  9. Exercise - 1 A package-filling process at a Cement company fills bags of cement to an average weight of µ but µ changes from time to time. The standard deviation is σ = 3 pounds. A sample of 25 bags has been taken and their mean was found to be 150 pounds. Assume that the weights of the bags are normally distributed. Find the 90% confidence limits for µ.

  10. STEP BY STEP Critical Value Approach to Hypothesis Testing 1- State Ho and H1 2- Choose level of significance, α Choose the sample size, n 3- Determine the appropriate test statistics and sampling distribution. 4- Determine the critical values that divide the rejection and non-rejection areas. 5- Collect the sample data, organize the results and compute the value of the test statistics. 6- Make the statistical decision and state the managerial conclusion If the test statistics falls into non-rejection region, DO NOT REJECT Ho If the test statistics falls into rejection region, REJECT Ho The managerial conclusion is written in the context of the real world problem.

  11. Exercise –Hourly wage The president of a company states that the average hourly wage of his/her employees is 8.65 TRL. A sample of 50 employees has the distribution shown below. At α=0.05, is the president’s statement believable? Assume σ=0.105 TRL M fM fM2 _______ 8.39 16.78 140.7842 8.48 50.88 431.4624 8.57 102.84 881.3388 8.66 155.88 1349.9208 8.75 87.5 765.625 8.84 17.68 156.2912 431.56 3725.4224 Class Freq. 8.35-8.43 2 8.44-8.52 6 8.53-8.61 12 8.62-8.70 18 8.71-8.79 10 8.80-8.88 2 Total: 50

  12. Exercise – Athletic Shoes A researcher claims that the average cost of men`s athletic shoes is less than 80 USD. He selects a random sample of 35 pairs of shoes from a catalog and finds the following costs. Is there enough evidence to support the researcher`s claim at α = 0.10. ∑x =2630 ∑(x−x̄)²= 12824

  13. Exercise –INFECTIONS A medical investigation claim that the average number infections per week at a hospital is 16.3. A random sample of 10 weeks had a mean number of 17.7 infections. The sample standard deviation is 1.8 Is there evidence to reject the investigator’s claim at α = 0.05? Assume the variable is normally distributed .

  14. Exercise –Internet Access Z-test for Proportion Of 2000 adults, 1540 said that they wanted Internet Access so, they could check personal e-mail while on vacation. A survey conducted in the previous year indicated that 75% of adults wanted Internet Access. Is there evidence that the percentage of adults who wanted Internet Access has changed from the previous year

  15. Exercise – Starting Salary A job placement director claims that the average starting salary for nurses is 24,000 USD. A sample of 10 nurses` salaries has a mean of 23,450 USD and a standard deviation of 400 USD. Is there enough evidence to reject the director`s claim at α=0.05?

  16. Exercise – Attorney Advertisements An attorney claims that more than 25% of all lawyers advertise. A sample of 200 lawyers in a certain city showed that 63 had used some form of advertising. At α = 0.05, is there enough evidence to support the attorney`s claim? Use the p-value method.

  17. Exercise – Sugar Sugar is packed in 5 kg bags. An inspector suspects the bags may not contain 5 kg. A sample of 50 bags produces a mean of 4.6 kg and a standard deviation of 0.7 kg. Is there enough evidence to conclude that the bags do not contain 5 kg as stated at α = 0.05? Also find the 95% CI of the true mean.

  18. H0:µ = 3.5 and H1 : µ > 3.5 A researcher thinks that if expectant mother use vitamin pills, the birth weight of the babies will increase . The average birth weight of the population is 3.5 kg.

  19. H0:µ = 18 and H1 : µ < 18 An engineer hypothesizes that the mean number of defects can be decreased in a manufacturing process of compact disks by using robots instead of humans for certain tasks. The mean number of defective disks per 1000 is 18.

  20. H0:µ =73 and H1 : µ≠73 A psychologist feels that playing soft music during a test will change the results of the test. The psychologist is not sure whether the grades will be higher or lower. In the past, the mean of the scores was 73.

  21. REJECT H0 ACCEPT H0 H0 IS TRUE H0 IS FALSE If the null hypothesis is true and accepted or false and rejected the decision is in either case CORRECT. If the null hypothesis is true and rejected or false and accepted the decision is in either case in ERROR.

  22. Example : Fast-Food Restaurant You are manager of a fast-food restaurant. You want to determine whether the waiting time to place an order has changed in the past month from its previous population mean value of 4.5 minutes. A-) State the null Hypothesis and Alternative Hypothesis From past experience, you can assume that the population is normally distributed with the standard deviation of 1.2 minutes. You select a sample of 30 orders during one-hour period. The sample mean is 5.1 minutes. B- Determine whether there is evidence at the 0.05 level of significance that the population mean waiting time to place an order has changed in the past month from its previous population mean value of 4.5 minutes. C- Find and use p-Value approach to test the Hypothesis.

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