The viscosity of a liquid detergent is supposed to average 800 centistokes at 25°C. A random sample of 16 batches of detergent is collected, and the average viscosity is 812. Suppose we know that the standard deviation of viscosity is σ = 25 centistokes. (a) State the hypotheses that should be tested. (b) Test these hypotheses using α = 0.05. What are your conclusions?
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The viscosity of a liquid detergent is supposed to average 800 centistokes at 25°C. A random sample of 16 batches of detergent is collected, and the average viscosity is 812. Suppose we know that the standard deviation of viscosity is σ = 25 centistokes.
(a) State the hypotheses that should be tested.
(b) Test these hypotheses using α = 0.05. What are your conclusions?
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- (11.)Perform the test of hypotheses indicated, using the data from independent samples given. Use the p value approach. (The p-value can be only approximated.) a. Test Ho : H - Hz = 50 vs. Ha : µ, - u, > 50 @a = 0.01: = lu n1 = 30, x1 = 681 s1 = 8 n2 = 27, T2 = 625, 82 = 8 %3D b. Test Ho : 41 – Hz = 35 vs. Ha : Hi – Hy # 35@a = 0.10: n1 = 36, T1 = 325, 81 = 11 n2 = 29, T2 = 286. s2 = 7A random sample of n = 36 scores is selected from a normal population with a mean of μ = 60. After a treatment is administered to the individuals in the sample, a researcher finds the sample mean is M = 52. Use α = .05 and show every step of hypothesis test. a. If the population standard deviation σ = 18, is the sample mean sufficient to conclude that the treatment has a significant effect? b. If the population standard deviation σ = 30, is the sample mean sufficient to conclude that the treatment has a significant effect? Just show step 3 & 4 c. Comparing your answers of parts a and b, explain how the magnitude of the standard deviation influences the outcome of a hypothesis test.Suppose you have a sample of size n for variables X and Y. The sample covariance of X and Y is Cov(X,Y) = 1,000, the sample standard deviation for X is Sx=20 and the sample standard deviation for Y is SY=75. What is the sample correlation coefficient, r?
- x̅ = 50, µ =43, σ= 12 and n=16 conduct a two-tailed z-test. Use α = .01.Juan wants to estimate a population mean age of residents of a retirement community. Based on previous evidence, he believes the population standard deviation is approximately σ=7.4σ=7.4 years. Juan would like to be 99% confident that his estimate is within 1.6 years of the true population mean, and asks you to help him determine the appropriate minimum sample size. How large of a sample size should Juan use?A statistician has a random sample of 30 observations from a population which has a normal distribution with a standard deviation of 5. These data are used to test the hypotheses H : μ = 0, H, :μ + 0, where is the mean of the population. A 5% significance level will be used. fl (a) Calculate the power of an appropriate test when the true value of the population mean is 2. Give your answer to 3 dp. (b) When the true value of the population mean is 3, the power of the test at the 5% level is 0.908 (to 3 dp). Give an explanation of what this means in terms of hypothesis testing. (c) If the significance level of the test described in part (b) is increased from 5% to 10% what effect will this have on the power? Explain your answer.
- The nicotine content in cigarettes of a certain brand is normally distributed. The brand advertises that the mean nicotine content of their cigarettes is µ = 1.5, but measurements on a random sample of 100 cigarettes of this brand gave a mean of ?̅= 1.53 and s = 0.95. Is this evidence that the mean nicotine content is actually higher than advertised? 1. State the appropriate null and alternative hypotheses. H0: ? = 1.5 Ha: ? > 1.5 2. Should you use the z or t test? t – do not have sigma 3. Compute the test statistic to test your hypotheses. (report to 2 decimal places) ? = 1.53−1.5 0.95 √100 ⁄ = 0.32 4. Find the appropriate range of p-value for your test. P-value: a. Less than 0.005 b. Between 0.005 and 0.01 c. Between 0.01 and 0.025 d. Between 0.025 and 0.05 e. Greater than 0.05A simple random sample of size n= 15 is drawn from a population that is normally distributed. The sample mean is found to be x= 30.2 and the sample standard deviation is found to be s = 6.3. Determine if the population mean is different from 24 at the a= 0.01 level of significance. Complete parts (a) through (d) below. (a) Determine the null and alternative hypotheses. Ho: V24 H1: V24 (b) Calculate the P-value. P-value = (Round to three decimal places as needed.) (c) State the conclusion for the test. O A. Reject H, because the P-value is less than the a = 0.01 level of significance. O B. Reject H, because the P-value is greater than the a= 0.01 level of significance. OC. Do not reject H, because the P-value is greater than the a= 0.01 level of significance. O D. Do not reject H, because the P-value is less than the a = 0.01 level of significance. (d) State the conclusion in context of the problem. There sufficient evidence at the a = 0.01 level of significance to conclude that the…A simple random sample of size n= 15 is drawn from a population that is normally distributed. The sample mean is found to be x= 25.9 and the sample standard deviation is found to be s=6.3. Determine if the population mean is different from 24 at the a = 0.01 level of significance. Complete parts (a) through (d) below. (a) Determine the null and alternative hypotheses. Ho: 24 H,: V24 (b) Calculate the P-value P-value = (Round to three decimal places as needed.) (c) State the conclusion for the test. O A. Reject Ho because the P-value is greater than the a = 0.01 level of significance. O B. Rejeci Question Viewer P-value is less than the a = 0.01 level of significance OC. Do not reject Ho because the P-value is greater than the a= 0.01 level of significance. O D. Do not reject Ho because the P-value is less than the a = 0.01 level of significance. (d) State the conclusion in context of the problem. There V sufficient evidence at the a= 0.01 level of significance to conclude that the…
- A sample of n sludge specimens is selected and the pH of each one is determined. The one-sample t test will then be used to see if there is compelling evidence for concluding that true average pH is less than 7.0. What conclusion is appropriate in each of the following situations? USE SALT (a) n = 8, t= -2.8, a = 0.05 O Reject the null hypothesis. There is sufficient evidence that the true average pH is less than 7.0. O Reject the null hypothesis. There is not sufficient evidence that the true average pH is less than 7.0. O Do not reject the null hypothesis. There is sufficient evidence that the true average pH is less than 7.0. O Do not reject the null hypothesis. There is not sufficient evidence that the true average pH is less than 7.0. (b) n = 15, t= -3.5, a = 0.01 O Reject the null hypothesis. There is sufficient evidence that the true average pH is less than 7.0. O Reject the null hypothesis. There is not sufficient evidence that the true average pH is less than 7.0. O Do not…A researcher wishes to see if there is a difference in the manual dexterity of athletes and that of band members. Two random samples of 30 are selectedfrom each group and are given a manual dexterity test. The mean of the athletes’ test was 87, and the mean of the band members’ test was 92. The population standard deviation for the test is 7.2. At α = 0.01, is there a significant difference in the mean scores?A simple random sample of size n=40 is drawn from a population. The sample mean is found to be 107.6, and the sample standard deviation is found to be 20.2. Is the population mean greater than 100 at the α=0.025 level of significance? Determine the null and alternative hypotheses. H0: mu equals 100μ=100 mu less than 100μ<100 mu equals 100μ=100 mu greater than 100μ>100 mu less than 107.6μ<107.6 mu equals 107.6μ=107.6 mu greater than 107.6μ>107.6 H1: mu greater than 100μ>100 mu less than 100μ<100 mu equals 100μ=100 mu greater than 100μ>100 mu less than 107.6μ<107.6 mu equals 107.6μ=107.6 mu greater than 107.6μ>107.6 Compute the test statistic. t 0t0 t 0t0 z 0z0 = (Round to two decimal places as needed.) Determine the P-value. The P-value is . (Round to three decimal places as needed.) What is the result of the hypothesis test? the null hypothesis because the P-value is the level of significance.…