(b) The following data is obtained from a sample. n- 50 Ex- 2685 E-144346 (1) Find unbiased estimates for the population mean and variance. (11) Calculate a 99% confidence interval for the mean u. In a public opinion poll, 250 randomly chosen voters were interviewed and 90 of them said they would vote for 'PPM' party in the next general elections. The leader of the party states that 40% of all the voters support his party. Test at 5% level whether the leader is overstating his support
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- A researcher wants to examine different online teaching environments by collecting data on 20 students. Half of the students had synchronous class while the other half had asynchronous class. For the students who had the synchronous class, they scored an average of 80 on the final exam with a sample variance of 10. For the students who had the asynchronous class, they scored an average of 78 on the final exam with a sample variance of 18. Determine if there is a significant difference between the average final exam score between the two groups of students. Use a significance level of 5%. What is the null hypothesis? Group of answer choices: A.) The average final exam score for the asynchronous class is higher than the synchronous class. B.) There is a difference in the average final exam score between the asynchronous class and synchronous class. C.) The average final exam score for the asynchronous class is lower than the synchronous class. D.) There is no difference in the…A number of 28 university students who smokes completed a questionnaire inquiring their smoking history and behavior. The result shows that the average smoking initiation age of this group is 21.6 years with a variance of 18.49. Based on past record, the smoking initiation age of university student has a mean of 20.74 years with a standard deviation of 5.1 years. Conduct a necessary analysis to determine if the smoking initiation age remain the same as the previous record. Use 4% level of significance.Every year, all incoming high school freshmen in a large school district take a math placement test. For this year’s test, the district has prepared two possible versions: Version 1 that covers more material than last year’s test and Version 2 test that is similar to last year’s test. The district suspects that the mean score for Version 1 will be less than the mean score for Version 2. To examine this, over the summer the district randomly selects 90 incoming freshmen to come to its offices to take Version 1, and it randomly selects 75 incoming freshmen to come take Version 2. The 90 incoming freshmen taking Version 1 score a mean of 113.0 points with a standard deviation of 16.8 . The 75 incoming freshmen taking Version 2 score a mean of 117.0 points with a standard deviation of 18.5 . Assume that the population standard deviations of the test scores from the two versions can be estimated to be the sample standard deviations, since the samples that are…
- Medical researchers are interested in determining the relative effectiveness of two drug treatments on patients with a chronic mental illness. Treatment 1 has been around for many years, while treatment 2 has recently been developed based on the latest research. The researchers chose two independent test groups. The first group had 9 patients, all of whom received treatment and had a mean time until remission of 166 days, with a standard deviation of 8 days. The second group had 15 patients, all of whom received treatment 2 and had a mean time until remission of 161 days, with a standard deviation of 9 days. Assume that the populations of times until remission for each of the two treatments are normally distributed with equal variance. Can we conclude, at the 0.05 level of significance, that u, the mean number of days until remission after treatment 1, is greater than u,, the mean number of days until remission after treatment 2? Perform a one-tailed test. Then complete the parts…A z-test is to be performed for a population mean. Express the decision criterion for the hypothesis test in terms of x. That is, determine for what values of x the null hypothesis would be rejected. ala After training intensively for six months, John hopes that his mean time to run 100 meters has decreased from last year's mean time of 11.8 seconds. He performs a hypothesis test to determine whether his mean time has decreased. Preliminary data analyses indicate that it is reasonable to apply a z-test. The hypotheses are Ho:u= 11.8 seconds H:u11.64 O Reject H, if x 11.61 Submit Assignment 2021 McGraw-Hill Education. All Rights Reserved. Terms of Use | Privacy IIBelow is the summary A tutorial school has been running IELTS mock examination for many years. presented by the tutorial school related to the IELTS mock examination in one of the many online classes selected randomly in year 2022. IELTS score in mock examination Number of students <4 5 2 5 7 15 8 10 3 A report presented by this tutorial school 5 years ago indicated that the population mean score of IELTS mock examination was 7.05 points and ihe population proportion of students got 7 points or above was 0.67. (a) Construct a 95% confidence interval estimate of population mean score a student get in the IELTS mock examination in 2022. (b) Test, at 1% level of significance, if the population proportion of students get 7 points or above in 2022 is higher than that in year 2017. (The report must include the (i) null hypothesis and alternative hypothesis, (ii) rejection region(s), (iii) calculation of test statistics, and (iv) conclusion.) (c) If the confidence interval estimate in part…
- The time to complete the Advanced Placement (AP) Statistics Exam in previous years is normally distributed with an average time of 2.4 hours. Because of school closures due to COVID-19, the College Board offered an at-home test for the 2020 AP Statistics Exam. A teacher feels that students, on average, will have a different completion time for the at-home exam. They take a random sample of 25 students that took the exam and their mean time was 2.74 hours with a standard deviation of 0.25 hours. Test to see if the mean time has significantly changed using a 5% level of significance. Give answers to at least 4 decimal places. What are the correct hypotheses? Ho: M H₁: P Based on the hypotheses, find the following: Test Statistic t = Critical-Value t = ± 2.4 #v 2.4 o hours hoursFifteen years ago, a complete survey of all undergraduate students at a large University indicated that the average student smoked 7.7 cigarettes per day. Th director of the student health center wishes to determine whether the incidence of cigarette smoking at his University has lessened over the fifteen year period. He obtains the following results (in cigarettes smoked per day) from a random sample of 9 students. 6.1, 9.2, 5, 6.3, 4.8, 3.2, 7.6, 8.1, 9. Test the null hypothesis at the .05 level significane.The Substance Abuse and Mental Health Services Administration (SAMHSA, 2017) estimates that 10.9% of the population of the United States age 18–24 had an episode of depression in the previous 12 months. Suppose a researcher takes a random sample of 225 United States adults aged 18–24. Determine the value of the sample proportion, p, such that 5% of samples of 225 United States adults age 18–24 are greater than p. You may find software or a z-table useful. Give your answer precise to three decimal places. p = II
- In a comparison between the mean waiting time of the patients in the hospitals of Giza and Alexandria governments the minister of Health randomly selected 60 hospitals from Giza government and their mean waiting time was 30 minutes and the previous reports showed that the variance was 10 minutes. Also a sample consist of 50 hospitals from Alexandria governments was selected and their mean waiting time of this sample was 15 minutes and from previous reports the variance was 5 minutes. 1-Construct the 95% C.I for the difference between the average waiting time in Giza & Alex2- Without any computations, discuss fully and precisely what will happen to the results you obtained in part (1) if the confidence level changed to be 99% instead of 95%. Give the reason for your answerThe time to complete the Advanced Placement (AP) Statistics Exam in previous years is normally distributed with an average time of 2.6 hours. Because of school closures due to COVID-19, the College Board offered an at-home test for the 2020 AP Statistics Exam. A teacher feels that students, on average, will have a different completion time for the at-home exam. They take a random sample of 26 students that took the exam and their mean time was 2.73 hours with a standard deviation of 0.25 hours. Test to see if the mean time has significantly changed using a 5% level of significance. Give answers to at least 4 decimal places. What are the correct hypotheses? Ho: Select an answer ✓ H₁: Select an answer ✓ Test Statistic t = ? ✓ Critical-Value t = ± ? ✓ hours Based on the hypotheses, find the following: hours Shade the sampling distribution curve with the correct critical value(s) and shade the critical regions. The arrows can only be dragged to t-scores that are accurate to 1 place after…2. A principal of high school was concerned with amount of time her students devote to working at after-school jobs. She randomly selected 25 students, obtained their working hours for 1 week and computed x = 12.5 hours and s = 4.5 hours. She claims that her students work significantly more than the mean of 10.7 hours from a study conducted by the National Association of State High School Association. Test her claim by using the 5% level of significance.