Random samples that are drawn independently from two normally distributed populations yielded the following statistics. Group 1 Group 2 n¡ = 17 n2= 16 x= 291.5 X2=279.2 s= 1296 s5= 2641.96 (The first row gives the sample sizes, the second row gives the sample means, and the third row gives the sample variances.) Can we conclude, at the 0.10 significance level, that the two population variances, of and o,, differ? Perform a two-tailed test. Then complete the parts below.
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- You 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?1. Tim Hortons wanted to estimate the difference in the mean amounts of caffeine in two brands of coffee. They took a sample of 18-lbs jars of Brand I and another sample of 13-lbs jars of Brand II coffee. The following summary data (sample statistics) are collected? nį = 10 x, = 23 S1 = 3 Brand I Brand II n2 = 12 x2 = 25 S2 = 4 Assume that the two populations are normally distributed. A. Test at 5 % level of significance, whether there is a difference in the mean amounts of caffeine between the 2 brands of coffee. B. Construct a 95% Confidence Interval to estimate the difference in the mean amounts of caffeine in 2 brands of coffee. C. Does the result in part b) confirm your findings from part a)?A researcher takes sample temperatures in Fahrenheit of 16 days from San Francisco (Group 1) and 22 days from Atlanta (Group 2). Test the claim that the mean temperature in San Francisco is less than the mean temperature in Atlanta. Use a significance level of a = 0.10. Assume the populations are approximately normally distributed with unequal variances. You obtain the following two samples of data. Round answers to 4 decimal places. San Francisco 77.4 94.8 77 80.9 84 Ho: M₁ 73.4 84.9 92 60.6 83.6 92.5 76.3 93.4 87.2 81.5 70.4 What are the correct hypotheses? Note this may view better in full screen mode. Select the correct symbols for each of the 6 spaces. Atlanta 85.4 92.8 80.2 87.9 80.6 77.9 72.9 75.9 72.1 76.7 80.4 92.5 75.9 72.1 97.7 89.2 88.1 80 92.2 86 96.2 91.9 p-value H₁: M₁ Based on the hypotheses, find the following: Test Statistic = -0.635 X = 0.2494 × OH₂ The p-value is greater than alpha OF H₂ to alpha. The correct decision is to fail to reject the null hypothesis or The…
- The aim of a study is to test the ratio of variances in the weight of two groups of rats being under a certain drugs A ( group 1) and B ( group 2) . A random sample of 16 rats was selected from group land 13 rats from group 2, Then their weight were recorded. The results are shown in the following table n Mean Median sd group 1 16 3.5 3.0 1.05 group 2 13 2.20 2.0 1.15 F15,12,0.05 = 0.404 F 19,16,0.025 = 0.386 F16,10,0.025 =0.335| F16,10,0.05 =0.401 F15,12,0.1 =0.496 F19,16,0.05 =0.451 F10,16,0.025 = 0.286 F 12,15,0.05 =0.382 F16,19,0.025 = 0.371| F10,16,0.05 = 0.354 F12,15,0.1 =0.475 F16,19,0.05 = 0.437| Construct a 95% confidence interval for the ratio of the variances. [ Hint: because of the rounding select the closest interval ] O a. None of these O b. [ 2.488, O0.238 ] O c. [ 2.160 , 0.309] O d. [2.063 , 0.318]A researcher takes sample temperatures in Fahrenheit of 17 days from New York City and 18 days from Phoenix. Test the claim that the mean temperature in New York City is different from the mean temperature in Phoenix. Use a significance level of α=0.05. Assume the populations are approximately normally distributed with unequal variances. You obtain the following two samples of data. New York City Phoenix 99 94.2 95.5 72 93.2 86.8 102 122.1 85.4 114.4 80 94.7 86.4 89.7 75.4 104.7 79.5 77.6 83.4 106.8 64.3 98.6 65.5 91.5 87.7 82 104 97.7 74.3 64.9 59.5 82 82.8 72 116.2 The Hypotheses for this problem are: H0: μ1 = μ2 H1: μ1μ2 Find the p-value. Round answer to 4 decimal places. Make sure you put the 0 in front of the decimal. p-value =If other factors are held constant, which of the following sets of data would produce the largest value for an independent-measures t statistic? Question 3 options: The two samples both have n = 15, with sample variances of 20 and 25. The two samples both have n = 15, with variances of 120 and 125. The two samples both have n = 30, with sample variances of 20 and 25. The two samples both have n = 30, with variances of 120 and 125.
- A public health official in Okeechobee county needs to estimate the average diastolic blood pressure of all residents in Okeechobee county for a report that is being prepared for the Florida Department of Health.The official randomly selected 128 Okeechobee county residents and found that the mean diastolic blood pressure of the sample was 74 millimeters of mercury (mm Hg).Using a 98% confidence level, determine the margin of error, EE, and a confidence interval for the mean diastolic blood pressure of all Okeechobee county residents. From past research, it is known that the standard deviation of the distribution of all Okeechobee county residents' diastolic blood pressure is 5 mm Hg.Report the confidence interval using interval notation. Round solutions to two decimal places, if necessary.The margin of error is given by E=A 98% confidence interval is given by1. 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…. 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) = 0.01551. The tables below show the results of an independent samples t-test in SPSS conducted using the SPSS data we have been using this semester. Two groups ("Yes" and "No") are compared on their "final". Yes and no refer to whether they attended the review sessions or not. Review the results carefully and answer the questions below. (12 points) final final Attended review sessions? No Yes Equal variances assumed Equal variances not assumed Levene's Test for Equality of Variances F Group Statistics 219 Sig. N .641 35 70 t -2.693 d. What are the df for the t-test we use? 103 Mean Independent Samples Test -2.719 59.83 64.14 Std. Deviation 7.591 7.810 df Sig. (2-tailed) 103 .008 69.872 .008 e. Are the groups significantly different from each other? f. Which group scored higher? Yes Group No Group The two groups are not significantly different_ t-test for Equality of Means Mean Difference -4.314 Std. Error Mean -4.314 1.283 .933 Std. Error Difference 1.602 1.587 95% Confidence Interval of the…