Use the given statistics to complete parts (a) and (b) Assume that the populations are nomally distributed (a) Test whether u at the a=0.10 level of significance for the given sample data (b) Construct a 99% confidence interval about uy-2 Population 1 Population 2 21 497 62 19 483 122
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- Use the given statistics to complete parts (a) and (b). Assume that the populations are normally distributed. (a) Test whether u, P2 at the =0.05 level of significance for the given sample data. (b) Construct a 90% confidence interval about u, -P2- (a) Identify the nul and alternative hypotheses for this test. OA. Hg P2 OB. Hgi P=V2 H H2 OE Hoi V2 OC. H: H2 H "P2 OD. Hg 2 OF. H FV2 H: H2 Find the test statistic for this hypothesis test. (Round to two decimal places as needed.) Determine the P-value for this hypothesis test (Round to three decimal places as needed.) State the conclusion for this hypothesis test. O A. Do not reject Hg. There is suficient evidence at the a=0.05 level of significance to conclude that p,2 OB. Reject Hg. There is sufficient evidence at the a=0.05 level of significance to conclude that , 2 OC. Do not reject Hg. There is not sufficient evidence at the e0.05 level of significance to conclude that p, >H2 OD. Reject Hy. There is not suficient evidence at the a=…Two random samples of sizes n = 10 and n = 12 from chemistry course and physics course respectively, provided the following information about the final exam scores: Chemistry; Xe = 60, Physics; X, = 72, At a = 5%, can you conclude that %3D Se = 6.5 Sp = 4.0 a) the population variances are the same? b) the population means are the same? c) construct a 95% confidence interval for the difference in the population means.Assume that both populations are normally distributed. (a) Test whether u, +p, at the a=0.01 level of significance for the given sample data. (b) Construct a 99% confidence interval about µ1 - H2- Population 1 17 11.9 3.2 Population 2 17 13.8 2.4 O C. Ho P1 =P2 O D. Ho P1 H2 Hi iH1 =H2 Detemine the P-value for this hypothesis test. (Round to three decimal places as needed)
- Five samples of a ferrous-type substance were used to determine if there is a difference between a laboratory chemical analysis and an X-ray fluorescence analysis of the iron content. Each sample was split into two subsamples and the two types of analysis were applied, with the accompanying results. Assuming that the populations are normal, test at the 0.05 level of significance whether the two methods of analysis give, on the average, the same result. Determine the test statistic t=?The following data are on the dental measurements (distance in mm from the center of the pituitary to the pterygomaxillary fissure of 11 girls and 16 boys, all of whom were 16 years of age. a) From the SAS output, interpret the 95% confidence interval for the true average difference in dental measurements in the population of 16-year-old boy and 16-year-old girls (assume the population variances are equal).Independent random samples were selected from populations 1 and 2. Thesample sizes, means, and variances are as follows: Population 1 2 Sample Size 35 49 Sample Mean 12.7 7.4 Sample Variance 1.38 4.14 Find a 95% confidence interval for estimating the difference in thepopulation means (μ1 - μ1)
- The Body Mass Index (BMI) for a group of men and women was conducted thoroughly in a Town ABC. It was found the population variances for both groups are not similar. By using Table 5, solve a 99% confidence interval for the difference between mean BMI for men and women. Table 5: BMI data for Men and Women Men 11 28.9 6.4 Sample size Average Standard deviation Women 13 26.1 4A) find the critical value(s) assuming that the population variances are equal . B) Find the critical value (s) assuming that they population variances are not equal.b. A study conducted to compare the breakdown voltage in two insulating liquids, yields the voltage (kV) readings below, 62 58 Liquid 1 Liquid 2 53 47 56 55 50 59 56 60 59 46 44 47 51 53 i) Calculate the sample mean and sample variance of both liquids i.e. F1, I2, s,² and s,?. ii) Construct a 90% confidence interval for the difference in the mean breakdown voltage of both liquids. iii) Test at the 10% level of significance whether the mean breakdown voltage of liquid 1 exceeds that of liquid 2. Use the critical value approach.
- is a simple random sample. 1) Ten students in a graduate program were randomly selected. Their grade point averages (GPAs) when they entering entered the program were between 3.5 and 4.0. The following data were obtained regarding their GPAs on program versus their current GPAs. the Entering GPA 3.5 3.8 3.6 3.6 3.5 3.9 4.0 3.9 3.5 3.7 Current GPA 3.6 3.7 3.9 3.6 3.9 3.8 3.7 3.9 3.8 4.0A company manufactures a product by two different manufacturing processes (A and B). Because the management of this company is interested in estimating the difference between the average time it takes each process to produce the product, they selected independent samples from each process. The results of the samples and the population variances are shown below. Process A Process B Sample Size 32 35 Sample Mean (in minutes) 43 47 Population Variance (σ2) 64 70 a. Develop a 95% confidence interval estimate for the difference between the average time taken by the two processes. b. Is there conclusive evidence to prove that one process takes longer than the other? If yes, which process? Explain.The yield of alfalfa from a random sample of six test plots is 1.4, 1.6, 0.9, 1.9, 2.2,and 1.2 tons per acre. Assume the data can be looked upon as a sample from anormal population. Test at the 0.05 level of significance whether this supports thecontention that the average yield for this kind of alfalfa is 1.5 tones per acre.