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- Recently, the annual number of driver deaths per 100,000 for the selected age groups was as follows: Age Number of Driver Deaths per 100,000 16–19 38 20–24 36 25–34 24 35–54 20 55–74 18 75+ 28 Use the 4 steps of hypothesis testing to see if the prediction is significant with a criteria of alpha=.05 on the following data For each age group, pick the midpoint of the interval for the X value. (For the 75+ group, use 80.)The NAEP considers that a national average of 283 is an acceptable performance. Using α = .05, run a two-tail t-test for one sample to test Ho: µ=283 for the 2019 scores. Report the t-obt, df, and p-values. Would you reject the null hypothesis that the 2019 scores come from a population with average 283? If this is the case, does it come from a population from larger or smaller average?In a hypothesis test with hypotheses Ho: μ ≤ 54 and H1: μ > 54, a random sample of 24 elements selected from the population produced a mean of 58.6 and a standard deviation of 13.4. The test is to be made at the 10% significance level. Assume the population is normally distributed. What is the critical value of t ?
- 1. The following table illustrates the BMI for a number of patients recently enrolled in a study investigating the relationship between BMI and type 2 diabetes. Participant BMI (kg/m2) A 26.5 B 19.2 C 29.7 D 27.4 E 30.2 F 28.9 A) Assuming the participants can be considered to be normally distributed, and that they comefrom a population with a σ=2.4 kg/m2, calculate a 95% confidence interval for the mean BMI ofthe population for which they represent.B) Correctly interpret the confidence interval you found above.In Exercise 4.2.27, in finding a confidence interval for the ratio of thevariances of two normal distributions, we used a statistic S21/S22, which has an Fdistributionwhen those two variances are equal. If we denote that statistic by F,we can test H0 : σ21 = σ22 against H1 : σ21 > σ22 using the critical region F ≥ c. Ifn = 13, m = 11, and α = 0.05, find c.Which of the following can cause the usual OLS t statistics to be invalid (that is, not to have t distributions under H0)?(i) Heteroskedasticity.(ii) A sample correlation coefficient of .95 between two independent variables that are in the model.(iii) Omitting an important explanatory variable.
- .A sample of 9 measurements, randomly selected from a normally distributed population, resulted in x= 2.6, and s= 0.9 Conduct a hypothesis test to verify the claim that the population mean is greater than 2.5 . Use a=.05For a random sample of 50 measurements of X1, sample mean x ̄1 = 200, sample standard deviation s1 = 10. For X2, from a random sample of 50, sample mean x ̄2 = 190 and sample standard deviation s2 = 15. Assume that population distributions are approximately independent normal with unequal variances. Answer the following questions 1 through 3. 1. Construct a 90% confidence interval for μ1 − μ2. (i) State the assump- tions, (ii) show your work, and (iii) interpret the result in context of the problem. 2. Using the same samples, you want to test whether the difference between two population means is 5 or not at the significance level α = 0.1. H0 : μ1 − μ2 = 5 vs H1 : μ1 − μ2 ̸= 5. What would your conclusion be? Support your answer briefly. You don’t need to conduct the hypothesis test.The following table illustrates the BMI for a number of patients recently enrolled in a study investigating the relationship between BMI and type 2 diabetes. Participan t BMI (kg/m2) A 26.5 B 19.2 C 29.7 D 27.4 E 30.2 F 28.9 A) Assuming the participants can be considered to be normally distributed, and that they come from a population with a σ=2.4 kg/m , calculate a 95% confidence interval for the mean BMI ofthe population for which they represent.
- Assume that you have a sample of n1=8, with the sample mean X1=44, and a sample standard deviation of S1=5, and you have an independent sample of n2=14 from another population with a sample mean of X2=30 and the sample standard deviation S2=6. Using a significance level of α=0.025, what is the critical value for a one-tail test of the hypothesis H0: μ1≤ μ2 against the alternative H1: μ1>μ2? The critical value is ______ (Round to two decimal places as needed.)Consider the following data drawn independently from normally distributed populations: x−1x−1 = −1.6 x−2x−2 = −16.3 s12 = 8.9 s22 = 7.9 n1 = 23 n2 = 15 a. Construct the 95% confidence interval for the difference between the population means. Assume the population variances are unknown but equal. (Round all intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.) Confidence interval is __________ to ___________ b. Specify the competing hypotheses in order to determine whether or not the population means differ. multiple choice 1 H0: μ1 − μ2 = 0; HA: μ1 − μ2 ≠ 0 H0: μ1 − μ2 ≥ 0; HA: μ1 − μ2 < 0 H0: μ1 − μ2 ≤ 0; HA: μ1 − μ2 > 0 c. Using the confidence interval from part a, can you reject the null hypothesis? multiple choice 2 Yes, since the confidence interval includes the hypothesized value of 0. No, since the confidence interval includes the…You obtain a t comp of .975 in a two sample independent t test with alpha at .05. Is it significant?