The following three independent random samples are obtained from three normally distributed population with equal variances. The dependent variable is starting hourly wage, and the groups are the types of position (work study, co-op, internship). Software was used to conduct a one-way ANOVA to determine if the means are equal using a = 0.10.
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- One sample has n=7 and SS=35 and a second sample has n =17 and SS =45. What is the pooled variance for these two samples?A university is examining four methods to supplement instruction. The méthods have been analyzed in four separate studies, one for each method. In each study, the final exam scores of a control group of students who didn't receive any supplemental instruction were compared to those of a group who received the particular method of supplemental Instruction. A one-tailed, independent-samples t test (with the assumption of equal variances) was performed in each study to see if the mean for the supplemental instructional group was significantly greater than the mean for the control group. The table below summarizes the four studies. The subscript "1" refers to a control group, and the subscript "2" refers to a group receiving the particular method of supplemental instruction. The value s, is the pooled sample standard deviation. Note that this value was not reported in one of the studies. esc 1 Q Sample means Pooled sample standard deviation Sample sizes t test p-value Least estimated ES…Two suppliers manufacture a plastic gear used in laser printer.
- Consider the two sample t-test with equal variances and the paired t-test. These tests are equivalent to which experimental designs. State the designs and draw detailed comparison between them.A study compared three display panels used by air traffic controllers. Each display panel was tested for four different simulated emergency conditions. Twenty-four highly trained air traffic controllers were used in the study. Two controllers were randomly assigned to each display panel—emergency condition combination. The time (in seconds) required to stabilize the emergency condition was recorded. The following table gives the resulting data and the JMP output of a two-way ANOVA of the data. Emergency Condition Display Panel 1 2 3 4 A 17 25 31 14 14 24 34 13 B 16 22 28 9 12 19 31 10 C 21 29 32 15 24 28 37 19 Least Squares Means Estimates Panel Estimate Condition Estimate A 21.500000 1 17.166670 B 18.375000 2 24.500000 C 25.625000 3 32.166670 4 13.500000 Analysis of Variance Source DF Sum of Squares Mean Square F Ratio Model 11 1,458.3333 132.576 32.4675 Error 12 49.0000 4.083 Prob > F C. Total 23 1,507.3333…The gasoline price often varies a great deal across different regions across country X. The following data show the price per gallon for regular gasoline for a random sample of gasoline service station for three major brands of gasoline (A, B and C) located in 10 metropolitan areas across the country X. (Picture of the table is attached) a. State the null and alternative hypothesis for single factor ANOVA to test for any significant difference in the mean price of gasoline for the three brands.b. State the decision rule at 5% significance level.c. Calculate the test statistic.d. Based on the calculated test statistics decide whether any significant difference in the mean price of gasoline for three bands. Note: No excel ANOVA output allowed. Need to show all the steps in calculations
- The following three independent random samples are obtained from three normally distributed populations with equal variances. The dependent variable is starting hourly wage, and the groups are the types of position (work study, co-op, internship). Software was used to conduct a one-way ANOVA to determine if the means are equal using a = 0.10. Summary Statistics: Work Study 12.854 Co-op Internship ANOVA Table: Source Mean Standard Deviation Within Total 14.51 15.424 SS df 132.542 48 0.5487 Work Study vs. Co-op 1.8888 88.0834 46 1.9149 Work Study vs. Internship Co-op vs. Internship 0.449 MS Between 44.4586 2 22.2293 11.6086 8.3E-5 F -3.636 Sample Size Perform a Bonferroni test to see which means are significantly different. Round your answers to three decimal places, and round any interim calculations to four decimal places. Hint: Make sure to use Bonferroni's adjustment. -4.549 15 -1.755 24 10 P-value Test Statistic Adjusted P-value Statistically significant difference? 0.002 0.000…A behavioral researcher measures the stress response of mice exposed to scary animal pictures (cat, dog, lion, Cheshire cat) with a GABA sensor implanted in the brain. He uses randomly assigned 40 mice, 10 in each group. The researcher records the amount of stress after 30 seconds assuming that there is no difference in the response in whatever way the mouse is scared. The data is normally distributed. Means and variances are provided in the table below. Is there a difference in the response to scary animals. Group 1 - Cat n₁=10 m₁ = 10 s² 1= 1.8 Group 2 - Dog n2=10 m₂= 5.0 s²2= 3.4 Why is the scare effect so low in group 4? Group 3 - Lion n3=10 m3= 3.4 s²1= 2.5 Group 4 - Chesire Cat n4=10 m4= 2.4 s² 1= 1.6A leading American electric vehicle company wishes to determine whether four types of batteries for electric vehicles perform equally well. Four types of batteries for electric vehicle were randomly selected and installed in the three different models. The number of hours of use for each battery is given below. GRAPH PROVIDED VIA PICTURE A. Use the analysis of variance (ANOVA) procedure for completely randomized designs to determine whether there is a significant difference in the mean useful life of the four types of batteries. (Ignore the fact that there are different electric vehicle models.) Include the ANOVA table. B. Now consider the three different Models (X,Y,Z) and carry out the analysis of variance procedure for a randomized block design. Include the ANOVA table. C. Compare the results in parts (a) and (b). Discuss why the results in (a) is different from (b).
- The following three independent random samples are obtained from three normally distributed populations with equal variances. The dependent variable is starting hourly wage, and the groups are the types of position (work study, co-op, internship). Software was used to conduct a one-way ANOVA to determine if the means are equal using a = 0.01. Summary Statistics: Work Study 13.1813 Co-op 15.0517 Internship ANOVA Table: Source Between Within Mean Total 15.447 SS 42.1802 Standard Deviation df Work Study vs. Co-op 114.3338 48 Co-op vs. Internship 0.6592 1.6674 72.1536 46 1.5686 Work Study vs. Internship 0.4859 MS F Sample Size 15 24 2 21.0901 13.4452 2.5E-5 10 Perform a Bonferroni test to see which means are significantly different. Round your answers to three decimal places, and round any interim calculations to four decimal places. Test Statistic Adjusted P-value Statistically significant difference? P-value ? ? ?A new sleeping pill is advertised to increase the daily sleeping time of insomniacs by an average of 3.0 hours, with a variance of 0.27. A government group conducts an independent study on the new pill, claiming that the actual variance, o, of increase in sleeping time is higher than the advertised variance. The government group tests 20 insomniacs, chosen at random, with the new pill. The insomniacs report a mean daily sleeping increase of 2.9 hours, with a variance of 0.35. Is there enough evidence to conclude, at the 0.1 level of significance, that the government group is correct? Assume that the increase in the sleeping time provided by the new pill is normally distributed. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H,. p Họ :0 H :0 (b) Determine the…Two different types of catalysts are used in a chemical process. We want to conduct a hypothesis test to see if there is a difference in the yields at 5% significance level. Assume both populations are normaly distributed. To this end, we collect a simple random sample from each process. Assume equal variances. = = n-11, n=13,x,-90, x 91.4, 8, 4, 8=4.5