Consider the following competing hypotheses and relevant summary statistics: He: 0²/0² = 1 HA: 02/0² #1 Sample 1: ₁ = 45.3, s = 17.6, and m₁ = 6 Sample 2: ₂ = 48.1, så = 11.4, and n₂ = 4 Assume that the two populations are normally distributed. (You may find it useful to reference the appropriate table: chi-square table or Ftable) a. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) Test statistic < Prev. 6 of 12 Ħ Next >
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Consider the following competing hypotheses and relevant summary statistics:
H0: σ21/σ22�12/�22 = 1
HA: σ21/σ22�12/�22 ≠ 1
Sample 1: x¯�¯ 1 = 45.3, s21�12 = 17.6, and n1 = 6
Sample 2: x¯�¯ 2 = 48.1, s22�22 = 11.4, and n2 = 4
Assume that the two populations are
a. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)
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- The joint probability distribution is a probability distribution that defines the simultaneous behavior of at least one random variable. True FalseYou have an independent-measures study where your first sample has an s² = 9 and your second sample has an s? = 6. a. If your sample size for both samples is n= 5, find the sample variances and compute the pooled variance. b. On the other hand, if your samples have difference sample sizes, n1 = 5 and n2 13. Again, calculate the two sample variances and your pooled variance, c. Compare your answers from part a and b. Why are there differences?Violation of which assumption below for the two-factor ANVOA is not a cause for concern with large sample sizes? a. The populations from which the samples are selected must have equal variances. b. The populations from which the samples are selected must be normal. c. A violation of any assumption below would be a concern, even with large sample sizes. d. The observations within each sample must be independent.
- Consider the following 3 independent sample statistics (from Exercise 11.2.1, pg 454): Sample 1: Mean=43, SD=3.74, n=4, Sample 2: Mean=44, SD=4, n=3, Sample 3: Mean=34, SD=3.92, n=4. Compute the SS(between) and the SS(within). Type the three digit numbers, first representing the SS(between) and second the SS(within), separated by comma with no spaces; e.g., 350,278 SHOW THE STEPS I NEED A NEW ANSWER PLEASEThe following statistics are computed by sampling from three normal populations whose variances are equal: (You may find it useful to reference the table and the g table.) = 30.1, n₁ = 7; 2 = 35.5, n2 = 9; 3 = 40.9, n3 = 4; MSE = 25.0 a. Calculate 95% confidence intervals for H1 H2, H1 - Hз, and μ2 - μз to test for mean differences with Fisher's LSD approach. (Negative values should be indicated by a minus sign. Round final answers to 2 decimal points.) Population Mean Differences H1-H2 H1 H3 H2 H3 Confidence Interval Can we conclude that the population means differ?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…
- 1. What is the pooled variance for the following two samples? Sample 1: n - 8 and SS = 168 Sample 2: n = 6 and SS = 120 2. An independent-measures study comparing two treatment conditions produces a t statistic with df = 18. If the two samples are the same size, how many participants were in each of the samples? 3. Caroline and Mira are both really smart and do equally well in their psychology classes, but something happens to Caroline when she goes to their philosophy class. She just can't keep up, whereas Mira does even better. One of the independent variables is the student. True or FalseThe 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 ? ? ?The following three independent random samples are obtained from three normally distributed populations with equal variance. The dependent variable is starting hourly wage, and the groups are the types of position (internship, co-op, work study). Group 1: Internship Group 2: Co-op Group 3: Work Study 10.75 12.5 8.5 9.75 10.25 12.5 11.5 13 15.25 10.75 14.25 14.5 11.25 10.5 14 10.5 11 15 13.75 12.75 11.75 11.5 12.5 15.75 11.75 12.75 12 13.25 13.75 14 12.75 14.25 12.25 Conduct a one-factor ANOVA to determine if the group means are equal using α=0.01α=0.01. Group means:Group 1 mean: Group 2 mean: Group 3 mean: ANOVA summary statistics:F-test statistic = p=p= Conclusion: The sample data suggests there is a correlation in the starting hourly wages. There is not sufficient data to conclude that at least one group's average starting hourly wage is different. The sample data suggests the starting hourly wages are dependent There is not…
- 1. When applying one-way analysis of variance (ANOVA), all the following are key assumptions that should be satisfied EXCEPT: A. Samples are obtained independently and randomly from the population defined by the factor level. B. The mean of the samples taken from the population is always equal. C. The population at each factor level is approximately normally distributed. D. The population have a common variance. 4. The sum of squares for treatment (SST) measures: A. the variation above the k sample means. B. the variation below the k sample means. C. the variation between the k sample means. D. the variation within the k sample means. 5. Which of the following is NOT true for the F- distribution? A. It is generally skewed to the left. B. It has two degrees of freedom. C. It is continuous. D. Its units are non-negative. 2. Which of the following components in an ANOVA table are NOT additive? A. Mean squares B. Degree of freedom C. Sum of squares D. It is not possible to tell. 3. The…1. Six batteries taken at random from a large lot were subjected to life tests with the following results: 19, 22, 18, 16, 25, and 20 hours. Find the probability that the sample mean of x= 20 hours, as observed here, or one less than 20 hours could arise if the true mean of the lot of batteries is 21.5 hours, assuming a known variance of o = 10 hours, for the individual batteries in the lot. %3DThe 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 = 0.05. Summary Statistics: Work Study 13.1693 Co-op Internship ANOVA Table: Source Mean Standard Deviation Within Total 14.7388 15.441 Between 36.3088 SS df 96.765 48 Work Study vs. Co-op 0.6288 Co-op vs. Internship 1.5401 60.4562 46 1.3143 Work Study vs. Internship 0.2019 MS F Sample Size 15 24 2 18.1544 13.813 2.0E-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 ? ? ?