Consider the following set of samples obtained from two normally distributed populations whose variances are equal: Sample 1: 11.2 11.2 7.4 8.7 13.5 Sample 2: 11.7 9.5 15.6 16.5 11.3 Suppose that the samples were independent. Perform a test of hypothesis to determine if there is a difference in the two population means. Use a significance level of 0.05. Also Estimate the p-value approximately.
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Consider the following set of samples obtained from two
Sample 1: |
11.2 |
11.2 |
7.4 |
8.7 |
13.5 |
---|---|---|---|---|---|
Sample 2: |
11.7 |
9.5 |
15.6 |
16.5 |
11.3 |
Suppose that the samples were independent. Perform a test of hypothesis to determine if there is a difference in the two population
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- Given below are the analysis of variance (ANOVA) results from a Minitab display. Assume that you want to use a 0.01 significance level in testing the null hypothesis that the samples come from populations with the same mean. Source DF SS MS F P-val Factor 2. 2280.0 1140.0 7.9 5.39E–04 Error 144 20691.7 143.7 Total 146 22971.8 What can you conclude about the equality of the population means? (circle one) Reject H0 since the p-value is greater than the significance level. Fail to reject H0 since the p-value is greater than the significance level. Reject H0 since the p-value is less than the significance level. Fail to reject H0 since the p-value is less than the significance level.You work for a soft-drink company in the quality control division. You are interested in the variance of one of your production lines as a measure of consistency. The product is intended to have a mean of 12 ounces, and your team would like the variance to be as low as possible. You gather a random sample of 16 containers. Estimate the population variance at a 80% level of confidence. 11.82 11.83 11.85 11.89 11.9 11.97 12 12 12 12.01 12.02 12.04 12.05 12.11 12.16 12.18 Variance of Data: 0.012 Note: Round all values to 3 decimals and use those rounded values in subsequent calculations. a) Find the lower and upper x critical values at 80% confidence: Lower: Upper: b) Report your confidence interval for o?: Lower Bound: Upper Bound:Given below are the analysis of variance results from a Minitab display. Assume that you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean. Identify the p-value. Source DF SS MS F Factor 3 30 10.00 1.6 0.264 Error 50 6.25 Total 11 80 O A. 6.25 O B. 1.6 OC. 10.00 O D. 0.264 Click to select your answer. étv MacBook Air F10 F9 F7 30 888 *- F6 F3 esc F1 F2 & @ 7 4 5 2 3.
- . 3. A researcher is interested in knowing if preterm infants with late metabolic acidosis and preterm infants without the condition differ with respect to urine levels of a certain chemical. The mean levels, standard deviations, and sample sizes from the two samples are given below. Assuming that the populations have equal variances: a. Fill in the missing pieces of the Stata output. ttesti 38 8.5 3.5 32 6.85 2.6 X y Two-sample t test with A variances combined diff Obs Ho: diff=0 38 32 Sample With condition 70 diff mean(x) n 38 Without condition 32 Ha: diff |t|) = F [95% Conf. Intervall 7.349579 5.9126 6.98079 .1552544 t = degrees of freedom = 9.650421 7.7874 8.510638 3.144746 E b. What is the conclusion of your test? c. Use this output to construct a 99% confidence interval for the difference between the two means. 68 Ha: diff0 Pr(Tt) = 0.0155You wish to test the following claim (��) at a significance level of �=0.002. ��:�1=�2 ��:�1≠�2You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you also have no reason to believe the variances of the two populations are not equal. You obtain the following two samples of data. Sample #1 Sample #2 50.2 77.2 87.1 65 64.2 58.4 78 60.5 72.6 53.1 51.2 75.6 64.2 93.6 68.6 63.8 71.9 74.9 74.5 54.6 59.2 61.8 90.1 73.6 55.4 62.6 68.6 71.6 67.9 87.3 51.9 85.2 81.3 76.3 54 59.6 59.6 88.6 50.8 What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = What is the p-value for this sample? For this calculation, use the degrees of freedom reported from the technology you are using. (Report answer accurate to four decimal places.)p-value =A study was done using a treatment group and a placebo group. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.10 significance level for both parts. a. Test the claim that the two samples are from populations with the same mean. What are the null and alternative hypotheses? OA. Ho: H₁ H₂ H₁: Hq ZH₂ OC. Ho: H₁ H₂ H₁: Hy > H₂ The test statistic, t, is. (Round to two decimal places as needed.) (Round to three decimal places as needed.) The P-value is State the conclusion for the test. C... OB. Ho: H₁ H₂ H₁: Hy #H₂ OD. Ho: Hg #U2 H₁: HyChoose the appropriate statistical test. When computing, be sure to round each answer as indicated. A dentist wonders if depression affects ratings of tooth pain. In the general population, using a scale of 1-10 with higher values indicating more pain, the average pain rating for patients with toothaches is 6.8. A sample of 30 patients that show high levels of depression have an average pain rating of 7.1 (variance 0.8). What should the dentist determine? 1. Calculate the estimated standard error. (round to 3 decimals). [st.error] 2. What is thet-obtained? (round to 3 decimals). 3. What is the t-cv? (exact value) 4. What is your conclusion? Only type "Reject" or Retain"when applying ANOVA which of the following steps would be important: a. the standard deviation of all the populations involved in the experiment is constant. b. the sample size of each sample is atleast 10. c. the population group that are being considerded are not more than 5. d. calculating side- by- side box plots will give a good visual representation of the variance between and within treatments. e. the samples are coming from normally distributed populations.The accompanying table lists pulse rates. Use a 0.05 significance level and apply the methods of two-way analysis of variance. What is the conclusion? Click on the icon to view the data table. C State the null and alternative hypotheses in the test for the effect of an interaction between row and column factors. Ho: There is no interaction between gender and age. H₁: There is an interaction between gender and age. What is the value of the test statistic for this test? F = 3.32 (Round to two decimal places as needed.) What is the corresponding P-value of the test statistic, F, for this P-value= (Round to three decimal places as needed.) Pulse Rates for Gender and Age Over 30 Years of Age Under 30 Years of Age Female 78 103 78 63 61 98 81 98 91 95 77 75 73 65 71 78 61 71 74 55 Female Male 60 81 56 69 68 74 75 68 63 56 46 70 61 65 91 80 59 58 64 59 Male D XScientists measured the amount of drug in tablets produced at two different, independent sites. Scientists want to know whether there is any difference between the mean drug concentration in tablets produced at Site 1 and Site 2. Run the appropriate test in Excel, assuming the population variances are equal. Use an a = .05 significance level. Submit the...A study was done using a treatment group and a placebo group. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.01 significance level for both parts. a. Test the claim that the two samples are from populations with the same mean. What are the null and alternative hypotheses? OA. Ho: H₁ H₂ H₁: H₁ H₂ OC. Ho: H₁ H¹/₂ H₁: H₁Given below are the analysis of variance results from a stat software display comparing sample data for the meanmileage for 4 different types of cars. Assume that you want to use a 0.05 significance level in testing the null hypothesisthat the different samples come from cars with the same mileage. What can you conclude about the equality of the population means?Source DF SS MS F pFactor 3 13.500 4.500 5.17 0.011Error 16 13.925 0.870Total 19 27.425 12)What is the null and alternative hypothesis for this scenari?Based on this One Way Anova software analysis, would you reject of fail to reject the nul hypothesis?What does this result mean in context?SEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. 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