2. The lifetimes of two types of LEDs were compared, two samples were collected and the following are the results (in 1000 hours) n mean Type I st.dev. 25 56.8 4.3 Type II 18 54.6 3.6 Find a 95% confidence interval for the difference of the two means. Using the CI, test the hypothesis that the means are equal.
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- A study was conducted of 90 adult male patients following a new treatment for congestive heart failure. One of the variables measured on the patients was the increase in exercise capacity (in minutes) over a 4-week treatment The previous treatment regime had produced an average increase of μ = 2 minutes. The researchers wanted to evaluate whether the new treatment had increased the value of μ in comparison to the previous treatment. The sample data yielded ?̅ = 2.17 and ? = 1.05: Using α = 05, what conclusions can you draw about the research hypothesis?A group of students sampled water from 34 lakes in St. Joseph County. If the mean dissolvedoxygen level was 3.2 with a standard deviation of .57 find a 90% confidence interval for thedissolved oxygen levels in St Joseph County lakes.A2.2
- A medical researcher wishes to see whether the pulse rates of smokers are higher than the pulse rates of nonsmokers. Samples of 100 smokers and 100 nonsmokers are selected. The results are shown below. Smokers Nonsmokers X = 90 S1 = 5 nj = 100 X2 = 88 %3D S2 = 6 n2 = 100 a) Find a 99% confidence interval for the true mean difference in smokers pulse rates and nonsmokers pulse rates. b) At a = 0.05, can we conclude that the pulse rates of smokers is higher than the pulse rates on nonsmokers?A study was performed to determine whether men and women differ in repeatability in assembling components on a specific engine part. Random samples of 28 men and 25 women were selected, and each subject assembled the units. The two sample standard deviations of assembly time were S??? = 1.98 minutes and S????? = 2.31 minutes. Do we accept the claim that men and women differ in repeatability for this assembly task? Use α = 0.02. (Treat S??? ?? S1,??? S????? ?? S2) Find the: Parameter of interest: ? Null hypothesis: ? Alternative hypothesis: ? Test statistic: ? Reject H0 if: ? Computations: ? Conclusion: ?Listed below are systolic blood pressure measurements (mm Hg) taken from the right and left arms of the same woman. Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal. Use a 0.10 significance level to test for a difference between the measurements from the two arms. What can be concluded? Right arm Left arm 143 179 OA. Ho: H0 H₁: Hd=0 OC. Ho: P = 0 H₁: Hd 0 sufficient evidence to support the claim of a difference in measurements between the two arms.
- The following results come from two independent random samples taken of two populations. Sample 1 n₁ = 60 Sample 2 n₂ = 25 x₂ = 11.6 1 = 2.4 %₂ = 3 (a) What is the point estimate of the difference between the two population means? (Use x₁-x₂.) x₁ = 13.6 (b) Provide a 90% confidence interval for the difference between the two population means. (Use ₁ - X₂. Round your answers to two decimal places.) to (c) Provide a 95% confidence interval for the difference between the two population means. (Use x₁ - x₂. Round your answers to two decimal places.) to8/10Use technology and the StudentSurvey dataset to test whether the data provide evidence that there is a difference in the mean number of hours spent watching television per week between males and females. Click here for the dataset associated with this question. What are the hypotheses? Use subscripts 1 for females and 2 for males. :: u :: p :: Pi : P2 :: p :: x :: x1 :: = :: :: U2 :: x2 : p : P1 : P2 :: r Ho: ! I vs Ha: 1 ::
- The wrist extension in degrees was measured for each of 36 randomly selected individuals as they used a prototype of a new computer mouse. The results were xbar = 20.4 and s=1.5. The researchers wish to test Ho : u=20 versus Ha : u > 20 at the 10% level of significance. (Extension of more than 20o is known to increase the risk of injury under repeated use.) 3. The observed significance )the p-value) of the test is about: a) 0.055 b) 0.020 c) 0.455 d) 0.110 e) 0.010A researcher comparing the means of dependent samples consisting of 30 matched pairs and obtained a mean difference of 5 and a standard error of the mean difference of 2. The confidence interval for the mean difference was (1.6, 8.4). What confidence level was used in constructing the interval?A biology student measured the ear lengths of an SRS of 10 Mountain cottontail rabbits, and an SRS of 10 Holland lop rabbits. The ear lengths for the two samples are listed in the two tables attached (see attached image). (a) Calculate a 95% confidence interval for the difference in mean ear lengths between Mountain cottontail rabbits and Holland lop rabbits. Make sure to define which is “µ1” and which is “µ2.” (You can complete the calculations either by hand or using R, but remember to show all your work.) (b) Do Holland lop rabbits have longer ears on average than Mountain cottontail rabbits? Carry out a test of significance to answer this question. Show your work at each step. Don’t forget to state the hypotheses at the start (making sure to define all parameters), and to include a conclusion in terms of the original problem. (You can complete the calculations either by hand or using R, but remember to show all your work.)