Every year, the students at a school are given a musical aptitude test that rates them from 0 (no musical aptitude) to 5 (high musical aptitude). This year's results were: Aptitude Score Frequency 3 1 2 3 1 5 The mean () aptitude score: (Please show your answer to 1 decimal place.) The median aptitude score: The mode aptitude score: (Please separate your answers by ',' in bimodal situation. Enter DNE if there is no mode.)
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- An analysis was conducted by the Statistics Consulting Center atVirginia Polytechnic Institute and State University in which acertain treatment was applied to a set of tree stumps. The chemicalGarlon was used the with the purpose of regenerating the roots ofthe stumps. A spray was used with four levels of GarlonPage 23 of 23concentration. After a period of time the height of the shoots wasobserved. Does the concentration of Garlon has a significantimpact on the height of the shoots? Use α = 0.05.In 2019, investigators from Brown University would like to determine the relationship between nail polish remover and ovarian cancer in women. A cohort of n=1000 beauticians aged 18-64 years old was identified and followed up after five years. After the follow-up period, there were x = 20 new cases of breast cancer were diagnosed. It is known that the incidence computed in this study is equal to the incidence known in America at a 0.01 level of significance. Identify the appropriate test to be used and conclude using the 7 steps of hypothesis.Water samples are taken from water used for cool- ing as it is being discharged from a power plant into a river. It has been determined that as long as the mean tem- perature of the discharged water is at most 150°F, there will be no negative effects on the river’s ecosystem. To investigate whether the plant is in compliance with regu- lations that prohibit a mean discharge water temperature above 150°F, researchers will take 50 water samples at randomly selected times and record the temperature of each sample. The resulting data will be used to test the hypotheses H0: m = 150°F versus Ha: m > 150°F. In the context of this example, describe Type I and Type II er- rors. Which type of error would you consider more seri- ous? Explain.
- Suppose that 3000 drivers in Wakanda were randomly breath-tested on 21 April 2019 and 116 were above the limit of 0.05 blood- alcohol level. On 15 May 2019, 4000 drivers were tested and 98 were above this level What additional information would you require before trying to draw a conclusion from these data?In Semester 1 2020/2021 study session, Sara has registered three courses namely Statistics, Research Methodology and Educational Psychology. In this particular academic session, each course has 100 registered students (including Sara). Table 2 shows the Sara’s marks in Mid-Term Tests with the mean and standard deviation for each course: -table- a.Express EACH of the Sara’s marks in term of standardized score (viewed from the respective course). b.Based on the standardized scores in (a), identify which course: Sara performs best in the Mid-Term test Sara perform worst in the Mid-Term test c. A male student scored 2 standard deviations above the mean of the Mid-Term Statistics What is his actual mark? d.Let assume that the population distribution (i.e. test scores of all 100 registered course takers) of Mid-Term Statistics test is normal. If a student scores 39 in Statistics Mid-Term test, would he fall in Top 5% scorers? Explain your answer.The mean output of solar cells of three types is measured six times under random light intensity over a period of 5 minutes, yielding the results shown. Research question: Is the mean solar cell output the same for all cell types?
- Suppose a researcher is interested in the relationship between periodontal disease and a number of negative health outcomes. One outcome of particular interest to the researcher is hypertension (assume defined as systolic blood pressure above 140 mmHG). Suppose a team gathers a SRS of 348 participants with periodontal disease, and finds the sample average systolic blood pressure to be 157 mmHG. A) Using an assumed σ=16 mmHG, conduct a 1 sample Z test to determine if there is a relationship between periodontal disease and hypertension in this population. (Use α=0.05)An experiment was conducted to compare the effectiveness of four training programs, namely, A, B, C, and D in training assemblers of a piece of electronic equipment. Twenty employees were randomly selected and assigned to each program, that is, five employees per program. After completion of the training courses, each person was required to assemble four pieces of equipment, and the length of time (in secs) to complete the assembly was recorded. The summary of the data gathered is recorded in the table. At α=0.10, test for the hypothesis that the assembly times for people trained are the same for the four programs. A B C D x̄ 62.46 51.00 63.47 60.57 s 4.13 4.03 4.49 4.60 n 5 5 5 5 Pairwise Comparison Test 1 Given the hypotheses: H0:μ1=μ4 ; Ha:μ1≠μ4 Compute for the Tukey's q-statistic. Round off to the nearest hundredths: _________________ Given the hypotheses: H0:μ1=μ4; Ha:μ1≠μ4 What is the appropriate conclusion based on the computed q-statistic?…An experiment was conducted to compare the effectiveness of four training programs, namely, A, B, C, and D in training assemblers of a piece of electronic equipment. Twenty employees were randomly selected and assigned to each program, that is, five employees per program. After completion of the training courses, each person was required to assemble four pieces of equipment, and the length of time (in secs) to complete the assembly was recorded. The summary of the data gathered is recorded in the table. At α=0.10, test for the hypothesis that the assembly times for people trained are the same for the four programs. A B C D x̄ 62.46 51.00 63.47 60.57 s 4.13 4.03 4.49 4.60 n 5 5 5 5 Pairwise Comparison Test 1 Given the hypotheses: H0:μ1=μ4 ; Ha:μ1≠μ4 Compute for the Tukey's q-statistic. Round off to the nearest hundredths: _________________ Given the hypotheses: H0:μ1=μ4; Ha:μ1≠μ4 What is the appropriate conclusion based on the computed q-statistic?…
- An experiment was conducted to compare the effectiveness of four training programs, namely, A, B, C, and D in training assemblers of a piece of electronic equipment. Twenty employees were randomly selected and assigned to each program, that is, five employees per program. After completion of the training courses, each person was required to assemble four pieces of equipment, and the length of time (in secs) to complete the assembly was recorded. The summary of the data gathered is recorded in the table. At α=0.10, test for the hypothesis that the assembly times for people trained are the same for the four programs. A B C D x̄ 62.46 51.00 63.47 60.57 s 4.13 4.03 4.49 4.60 n 5 5 5 5 Pairwise Comparison Test 1 Given the hypotheses: H0:μ1=μ2 ; Ha:μ1≠μ2 Compute for the Tukey's q-statistic. Round off to the nearest hundredths: Pairwise Comparison Test 2 Given the hypotheses: H0:μ1=μ3 ; Ha:μ1≠μ3 Compute for the Tukey's q-statistic. Round off to the nearest hundredths:An experiment was conducted to compare the effectiveness of four training programs, namely, A, B, C, and D in training assemblers of a piece of electronic equipment. Twenty employees were randomly selected and assigned to each program, that is, five employees per program. After completion of the training courses, each person was required to assemble four pieces of equipment, and the length of time (in secs) to complete the assembly was recorded. The summary of the data gathered is recorded in the table. At α=0.10, test for the hypothesis that the assembly times for people trained are the same for the four programs. A B C D x̄ 62.46 51.00 63.47 60.57 s 4.13 4.03 4.49 4.60 n 5 5 5 5 1. What is the null and alternative hypothesis? 2. In the decision rule: Reject H0 if Fc>F0.10,(A,B)=C .Otherwise, fail to reject H0. What is the value for df for treatments, A? What is the value for df for error, B? What is the critical value, C? 3. Decision for the ANOVA…An experiment was conducted to compare the effectiveness of four training programs, namely, A, B, C, and D in training assemblers of a piece of electronic equipment. Twenty employees were randomly selected and assigned to each program, that is, five employees per program. After completion of the training courses, each person was required to assemble four pieces of equipment, and the length of time (in secs) to complete the assembly was recorded. The summary of the data gathered is recorded in the table. At α=0.10, test for the hypothesis that the assembly times for people trained are the same for the four programs. A B C D x̄ 62.46 51.00 63.47 60.57 s 4.13 4.03 4.49 4.60 n 5 5 5 5 Suppose it makes sense to conduct a post-hoc analysis. We will use Tukey's test to make pairwise comparisons between means. The decision rule for Tukey's test would be as follows: "Reject H0 if |qc|>q0.10,K,L=M . Otherwise, fail to reject H0." 1. What is the value for the number of…