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- A researcher wants to test the difference in the mean scores of two independent groups on a standardized test. Group 1 has a sample size of 40 and a mean score of 72, while Group 2 has a sample size of 50 and a mean score of 68. Is there a significant difference in the mean scores of the two groups?The median number of part-time employees at fast-food restaurants in a particular city wasknown to be 18 last year. City officials think the use of part-time employees may be increasing. A sample of nine fast-food restaurants showed that seven restaurants were employing more than 18 part-time employees, one restaurant was employing exactly 18 part-time employees, and one restaurant was employing fewer than 18 part-time employees. Can it be concluded that the median number of part-time employees has increased? Test using α = 0.05Suppose that 80% of 3–4-year-old children and 70% of5–8-year-old children in a village are vaccinated with QIVvaccine. Also assume that children who are not vaccinatedhave twice the incidence of influenza as the control groupin Table 3.7.3.29 What % of 3–4-year-old children in the village will getinfluenza?3.30 What % of 5–8-year-old children in the village will getinfluenza?3.31 Suppose we identify a 5–8-year-old child with influenzain the village but are uncertain whether the childwas vaccinated. If we make the same assumptions as inProblems 3.29–3.30, then what is the probability that thechild was vaccinated? (Hint: Use Bayes’ rule here.)
- A report in LTO stated that the average age of taxis in the Philippines is 9 years. An operationsmanager of a large taxi company selects a sample of 40 taxis and finds the average age of the taxis is8.2 years. The standard population is 2.3 years. At can it be concluded that the average ageof the taxis in his company is less than the national average?The department of education ran a very comprehensive study in the 1990's to determine the GPA of first generation college students (those who are the first in their family to go to college) in their freshman year. The mean GPA for first generation college students was stated in teh report to be 2.37 for males and 2.21 for females. In 2018, a consumer advocacy group is interested in whether the average GPA for first generation college females was still smaller than their male counterparts. Assume the GPA's are normally distributed. A. State the null hypothesis and the alternative hypothesis. Is the advocacy group interested in a one tail or two tail test (brief explanation)? B. Find the value of the test statistic and an associated p-value (or a range for teh p-value) if 25 males SAR yielded an average GPA 2.46 with a standard deviation of 0.16 and 25 females SAR yeilded an average GPA 2.39 with a standard deviation of 0.12. C. Determine if the test requires use of the Z table or…A researcher is interested in exploring the relationship between calcium intake and weight loss. Two different groups, each with 2828 dieters, are chosen for the study. Group A is required to follow a specific diet and exercise regimen, and also take a 500500-mg supplement of calcium each day. Group B is required to follow the same diet and exercise regimen, but with no supplemental calcium. After six months on the program, the members of Group A had lost a mean of 15.215.2 pounds with a standard deviation of 2.52.5 pounds. The members of Group B had lost a mean of 12.312.3 pounds with a standard deviation of 1.91.9 pounds during the same time period. Assume that the population variances are not the same. Construct a 95%95% confidence interval to estimate the true difference between the mean amounts of weight lost by dieters who supplement with calcium and those who do not. Let Population 1 be the amount of weight lost by Group A, who took a 500500-mg supplement of calcium each day,…
- A pharmaceutical company wants to test the effectiveness of a new drug for aparticular infectious disease. In a sample of patients with the disease, 24 wererandomly assigned to receive the new drug, while the remaining 16 patientswere given a placebo. The length of time the infectious disease lasted wasrecorded by a doctor for each patient. The sample mean for the group takingthe new drug was found to be 6.5 days and for the control group (taking theplacebo) the mean was 7.125 days. The (population) standard deviation ofrecovery times for people with the infectious disease is known to be 1.2 days.Test the claim that the drug reduces the time that an infectious disease lasts,at the 5% significance level. What is the p-value for this test? What assumptionsdo you need to make for this test to be valid?Suppose that the average waiting time for a patient at a physician's office is just over 29 minutes. In order to address the issue of long patient wait times, some physicians' offices are using wait-tracking systems to notify patients of expected wait times. Patients can adjust their arrival times based on this information and spend less time in waiting rooms. The following data show wait times (in minutes) for a sample of patients at offices that do not have a wait-tracking system and wait times for a sample of patients at offices with a wait-tracking system. Without Wait-Tracking System With Wait-Tracking System25 3365 916 1522 1835 1046 3212 927 312 1232 17A firm is studying the delivery times of two raw material suppliers. The firm is basically satisfied with supplierA and is prepared to stay with that supplier. However, if the firm finds that the mean delivery time of supplierB is less than that of supplier A, it will begin making raw material purchases from supplier B. Assume that 50independent samples from each supplier show the delivery time of supplier A to be 14 days with a standarddeviation of 3 days, while the delivery time of B is shown to be 12.5 days with a standard deviation of 2 days.Testing at a 0.05 level of significance, should the firm switch to supplier B or not? Compute for: null and alternative hypothesis in words level of significance and critical value/s and region (graph it please) compute the test statistic decision state the conclusion
- A young professor found out from a senior professor that psychology students in St. Alex University tend to do good in their Social Science subject, claiming that historically, the mean grade of psych students in the said course is 1.50. Curious if this claim was true, the young professor took a random sample of 9 students who took Social Science subject. Before collecting data, he was undecided about his own claim because he knew of some students who did really good in the course but has also encountered others who did poorly. He found that their mean grade for the course is 1.35 with a standard deviation of 0.50. Use the Test of Significance Approach in testing the young professor’s claim. a. Estimate μ at 90% confidence interval. b. Between z and t, which is more appropriate to use given the data? Why? c. What are the chances that your estimate of μ was wrong? Describe and explain a potential source of error to your estimate. d. Holding % of CI constant, what can you do to lower…Suppose, you work with the Quality Assurance Team of a Biscuit Company, and a customer complains that the mean weight of the biscuit packet you are selling is less than 250 gm when you have claimed it to be of weight 250 gm in the packet. To test the customer's claim, you sampled 25 biscuit packets and measured their weights. Let be the hypothesized mean weight of a biscuit packet that your company claims, and the null and alternative hypotheses have been formulated as: At a 5% level of significance (), what will be the conclusion from a one-sample t-test (assuming that all the assumptions of the test are satisfied) if you obtain a p-value of 0.023?Researchers are interested in the body fat measurements of elite women volleyball players from different countries test the claim that the mean body fat if elite women volleyball players from country 1 is smaller than the mean body fat if elite women volleyball players from. Country 2 at the 0.10 significance level