Question 1 (d) A standard method for determination of the carbon monoxide (CO) level in gaseous mixtures is known from many hundreds of measurements to have a standard deviation of 0.21 ppm CO. A moderation of the method yields a value for s of 0.15 ppm CO for pooled data set with 12 degrees of freedom. A second moderation, also based on 12 degrees of freedom, has a standard deviation of 0.12 ppm CO. Is either modification significantly more precise than the original?
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- QUESTION 9 The Department of Trade and Industry (DTI) conducted a survey to estimate the average number of employees per small and medium-sized enterprises (SME) in Free State. For a random sample of 144 SMEs in Free State, the DTI found that the average number of employees was 24.4. Assume that the population standard deviation is 10.8 employees and that the number of employees per SME is normally distributed. Using this information and rounding off the z or t values that you derive to 2 decimal places, the 95% confidence interval of the average number of employees per SME in Free State is for the lower limit andfor the upper limit. (Note: write your final answers to 3 decimal places and when writing your answer use "." (3.250) instead of "," (3,250) with no spaces between digits).Question 5 Consider the diameters of cylindrical parts manufactured on a computer-controlled lathe.a) Suppose that the mean of the diameters is known to be 0.1 millimetres. Give an upper bound to the probability that the diameter of new part will exceed 0.11 mm.b) Suppose that the mean is unknown but the standard deviation is known to equal 0.002 mm. What can be said about the probability that the diameter of a new part will be within 0.006 mm of the unknown mean for that run?c) How many new parts should be made so as to ensure, with probability at least 0.75, that the average diameter would be within 0.001 mm of the unknown mean? Assume each part is made independently.Question 1 Suppose the measures to ensure that all manufactured motor vehicles meet requirements with regards to carbon monoxide emission indicate that the standard deviation per unit volume of exhaust fumes must not be in excess of 0.03 percent carbon monoxide emission particles per unit volume. A random sample of ten newly manufactured motor vehicles are tested and the following carbon monoxide emissions are recorded: 0.23 0.27 0.31 0.25 0.30 0.29 0.32 0.26 0.24 0.22 Required to: a) Calculate the point estimate of the standard deviation of the carbon monoxide emissions? b) Calculate the 99% confidence interval estimate for the population variance of the carbon monoxide emissions and give an interpretation? c) Use the critical value approach, test a hypothesis at a 5% level of significance to determine whether the requirements are met? d) Suppose the level of confidence is reduced, what will happen to the answer in b)?
- Question 2 A manufacturer of sprinkler systems used for fire protection in office buildings claims that the true average system-activation temperature is 130 degrees. A sample of 9 systems when tested yields a sample average activation temperature of 131.08 degrees. If the distribution of activation times is normal with standard deviation 1.5 degrees, test at the 1% level of significance to see if the data shows evidence that is different from the manufacturers claim. (a) State the null and alternative hypotheses for the test. (b) What is the test statistic? (c) Calculate the value of the test statistic for this test. (d) Calculate the p-value for this test. (e) State the conclusion of this test. Give a reason for your answer.Question 6) The standard deviation value of the products in factory A is 25 g. The weight average of 300 products randomly selected from this factory was found to be 450 gr. The standard deviation value of the products in factory B is 46 gr and the weight average of 500 randomly selected products from the factory is 530 gr. Find and interpret the 99% confidence limits of the difference between the average weight of products in two different factories.Question #4 A consumer group claims that the mean minimum time it takes for a sedan to travel a quarter mile is greater than 14.7 seconds. A random sample of 23 sedans has a mean minimum time to travel a quarter mile of 15.5 seconds and a standard deviation of 2.08 seconds. At α=0.05 is there enough evidence to support the consumergroup's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. To Do: 1.) Identify the claim and state H0 and Ha. Do not round. 2.) The claim is the ___ hypothesis 3.) Use technology to determine the P-value. First calculate the standardized test statistic for the t-test, rounding to two decimal places. 4.) Decide whether to reject or fail to reject the null hypothesis. 5.) Interpret the decision in the context of the original claim. a) Interpret the decision in the context of the original claim. And fill in the blanks There is is not enough evidence at the ___%__ level of significance to ____ the claim…
- Question 2 A manufacturer of sprinkler systems used for fire protection in office buildings claims that the true average system-activation temperature is 130 degrees. A sample of 9 systems when tested yields a sample average activation temperature of 131.08 degrees. If the distribution of activation times is normal with standard deviation 1.5 degrees, test at the 1% level of significance to see if the data shows evidence that is different from the manufacturers claim. (d) Calculate the p-value for this test. (e) State the conclusion of this test. Give a reason for your answer.QUESTION 16 A researcher wants to compare the mean concentration of two medications considered biologically equivalent, i.e., two medications that are able to produce the same therapeutic effect at the same level of concentration in the blood. The group of individuals on medication one (n = 32) had a mean blood concentration of 21.7 micrograms per milliliter with a standard deviation of 8.7 micrograms per milliliter. The group of individuals on medication two (n= 32) had a mean blood concentration of 19.4 micrograms per milliliter with a standard deviation of 5.2 micrograms per milliliter. Construct and interpret a 95% confidence interval demonstrating the difference in means for the individuals on medication one when compared to the group of individuals on medication two. The researchers are 95% confident that the true mean difference in medication concentration levels between individuals on medication one and individuals on medication two is between 4.867 micrograms…QUESTION 5. (Data file included: Yes; In Sheet: Quality): Quality Associates, Inc., a consulting firm, advises its clients about sampling and statistical procedures that can be used to control their manufacturing processes. In one particular application, a client gave Quality Associates a sample of 800 observations taken while that client’s process was operating satisfactorily. The sample standard deviation for these data was 0.21; hence, with so much data, the population standard deviation was assumed to be 0.21. Quality Associates then suggested that random samples of size 30 be taken periodically to monitor the process on an ongoing basis. By analysing the new samples, the client could 5 quickly learn whether the process was operating satisfactorily. When the process was not operating satisfactorily, corrective action could be taken to eliminate the problem. The design specification indicated that the mean for the process should be 12. Corrective actions should be taken is the mean…
- QUESTION 5. (Data file included: Yes; In Sheet: Quality): Quality Associates, Inc., a consulting firm, advises its clients about sampling and statistical procedures that can be used to control their manufacturing processes. In one particular application, a client gave Quality Associates a sample of 800 observations taken while that client’s process was operating satisfactorily. The sample standard deviation for these data was 0.21; hence, with so much data, the population standard deviation was assumed to be 0.21. Quality Associates then suggested that random samples of size 30 be taken periodically to monitor the process on an ongoing basis. By analysing the new samples, the client could 5 quickly learn whether the process was operating satisfactorily. When the process was not operating satisfactorily, corrective action could be taken to eliminate the problem. The design specification indicated that the mean for the process should be 12. Corrective actions should be taken is the mean…Question 8: A computer company makes a new computer chip with an advertised processing power of 2.5 GHz and a standard deviation of 0.1 GHz.. QUESTION 12 In a survey of 120 publicly-traded companies, the average price-earnings ratio was 18.5 with a standard deviation of 8.2. When testing the hypothesis that the average energy use has decreased from the past value of 16.8, the p-value is 0.0116. Therefore, if you were testing the hypothesis (at the [a]% level of significance) that the average price-earnings ratio has decreased from the past, what is your conclusion concerning the null hypothesis? Reject the null hypothesis Fail to reject the null hypothesis