Confidence Level c = 0.90 and Sample Size n = 22 %3D %3D Left Right 1+ Level of Significance a Degrees of Freedom 1 Confidence Interval for Variance o (n- 1)s² (n – 1)s² XR XL
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- Sample data from a normal population are located in the Microsoft Excel Online file below. Use the data to answer the following questions for the σ unknown case. Sample Data 1 4 11 2 10 17 5 11 Confidence Coefficient=0.95 The point estimate of the population mean is (to 2 decimals) The standard deviation is (to 2 decimals) The margin of error is (to 1 decimal) The 95% confidence interval is (to 1 decimal)Independent random samples were selected from two quantitative populations, with sample sizes, means, and variances given below. Population 2 Sample Size 121 121 Sample Mean 3.2 5.7 Sample Variance 9.88 12.53 Construct a 90% confidence interval for estimating the difference in the population means (u, - H,). (Round your answers to two decimal places.) 3.2 X to 5.7 Construct a 99% confidence interval for estimating the difference in the population means. (Round your answers to two decimal places.) toIn order to estimate the difference between the average miles per gallon of two different models of automobiles, samples are taken and the following information is collected. Sample Size Sample Mean Sample Variance Model A a. 65 26 16 Model B 45 28 a 9 At 95% confidence, develop an interval estimate for the difference between the average miles per gallon for the two models. Is there conclusive evidence to indicate that one model gets a higher miles per gallon than the b. other? If yes, explain how you know this and which model is higher. If no, explain how you know that there is not enough evidence.
- Do men have a higher body temperature than women? Test the indicated claim about the means of two populations. Assume that the two samples are randomly selected, independent, the population standard deviations are not know and not considered equal. The table shows results from a study of body temperatures of men and women. At the 0.05 significance level, test the claim that men have a higher body temperature than women. Men Women n1 = 13 n2 = 16 xˉx̄1 = 97 °F xˉx̄2 = 95.17 °F s1 = 0.26 °F s2 = 0.57 °F What are the correct hypotheses? (Select the correct symbols and use decimal values not percentages.)H0: Select an answer x̄₂ μ₁ p p₂ μ₂ μ μ(men) p̂₁ x̄₁ σ₁² p₁ s₁² ? > < ≥ ≠ ≤ = Select an answer p̂₁ p₁ μ μ₁ p x̄₁ μ₂ s₁² x̄₂ μ(women) σ₁² p₂ H1: Select an answer σ₂² μ p̂₂ p₁ p p₂ x̄₁ μ(men) x̄₂ μ₂ μ₁ s₂² ? = ≤ > < ≥ ≠ Select an answer s₁² x̄₁ μ₂ μ p̂₁ x̄₂ σ₁² μ(women) p₁ p p₂ μ₁ Original Claim = Select an answer H₀ H₁ df = Based on the hypotheses, find…Dp2Analysis of Variance results: Where: Age > 5Responses: AgeFactors: Sex Response statistics by factor Sex n Mean Std. Dev. Std. Error female 121 10.490083 4.2222704 0.38384277 male 155 9.0806452 3.0091656 0.241702 ANOVA table Source DF SS MS F-Stat P-value Sex 1 134.98939 134.98939 10.466692 0.0014 Error 274 3533.79 12.897044 Total 275 3668.7794 Tukey HSD results (95% level) female subtracted from Difference Lower Upper P-value male -1.4094375 -2.2670907 -0.55178425 0.0014 In one complete sentence, interpret your confidence interval. Make sure in the interpretation it is clear the direction of the difference (i.e. which gender weighs more and by how much. Explain why a confidence interval provides more information to a tiger researcher than the results of a hypothesis test
- To construct a 95% confidence interval of variance using a sample of 18 the critical values used are __________ and _____________.Test the hypotheses shown below for a random sample with s = 140 and n= 28 at the 5% significance level. Họ: os 100 H,: o?> 100 Click the icon to view the upper critical values of Chi-square distribution table. For this test at the significance level a with sample variance s, hypothesized variance o, sample size n, and critical value x2: X-11- or x4g/2 and x11-g/2: what is the form of the decision rule? (n-1)s2 (n- 1)s? O A. Reject H, if > Xn-1g/2 or reject H, if 1-1,1-a/2 (n- 1)s2 O B. Reject Ho if (n- 1)s? Oc. Reject H, i -3/12Test the Variances.Assume both populations are normally distributed Họ: o Ho:0 = o HA:0 + 0 (Claim) %3D n1 = 6 , n2 = 14 a = 0.10 Two Sample F-Test for Variance Degrees of Freedom (Denominator) F-Test Statistic Degrees of Freedom (Numerator) dfN=n-1 F = Where sf> s Round all values to 3 decimal places a. The Critical Value FoD b. The Test Statistic Fonsider the following results for two independent random samples taken from two populations. Sample 1 Sample 2 n 1 = 50 n 2 = 30 x 1 = 13.1 x 2 = 11.2 σ 1 = 2.3 σ 2 = 3 What is the point estimate of the difference between the two population means? (to 1 decimal) Provide a 90% confidence interval for the difference between the two population means (to 2 decimals). Use z-table.( , ) Provide a 95% confidence interval for the difference between the two population means (to 2 decimals). Use z-table. If your answer is negative, enter minus (-) sign.( , )WALKING RUNNING Mean 7.181818182 7.3636364 Variance 4.563636364 6.4545455 Observations 11 11 Pooled Variance 5.509090909 Hypothesized Mean Difference 0 df 20 t Stat -0.181668105 P(T<=t) one-tail 0.428835886 t Critical one-tail 1.724718243 P(T<=t) two-tail 0.857671772 t Critical two-tail 2.085963447 If the t-Stat value is less than the t Critical two-tail value I can reject the null, right? I am still a little confused on what a few numbers represent.