Problem 2A chemical reactor system has been designed to perform optimally when operatedat 150°C. The hypothesis test that will be used for evaluating the operating temperature willrely on 10 successive temperature measurements and will assign a 95% confidenceinterval for the result. The reactor system is judged to have a standard deviation of ±3°C.Part A: Actual operating temperature of the process T[°C] = 152.90Part B: What is the probability that the hypothesis test for operating at 150°C describedabove will give a false acceptance (i.e., a type II error)?

Step 1: Actual Operating Temperature of the ProcessThe reactor is designed to operate optimally at…

Answered: Problem 2 A chemical reactor system has…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The concentration of a particular chemical in a processing plant is monitored regularly to check that it remains near the desired level of 8.25 mmol/L. Because of variability in the measure- ment system, this is checked by taking multiple samples over a short period of time and using the resulting measurements to carry out a formal statistical test. (The null hypothesis for this test is that the true mean concentration of the chemical is equal to the desired value, and you may assume that the measurements are Normally distributed.) The latest sample of eight measurements gave a sample average concentration (X) of 8.13 mmol/L and a sample standard deviation (s) of 0.16 mmol/L. Use this information and the statistical tables: Fawcett & Kent extract (Tables 1-6) to carry out the statistical test mentioned above, and report on what evidence (if any) there is to suggest that the mean concentration of the chemical has varied from the desired level.
Question 3 10 pts Suppose a sample of 30 ECC students are given an IQ test. If the sample has a standard deviation of 12.23 points, find a 90% confidence interval for the population standard deviation. FOLLOW THE PANIC METHOD Edit View Insert Format Tools Table 12pt ✓ v Paragraph B IUAT²:
Question 1We considered the differences between the temperature readings in January 1 of 1968 and 2008 at 51 locations in the continental US in Exercise 5.19. The mean and standard deviation of the reported differences are 1.1 degrees and 4.9 degrees respectively.(a) Calculate a 90% confidence interval for the average difference between the temperature measurements between 1968 and 2008.lower bound: degrees(please round to two decimal places)upper bound: degrees(please round to two decimal places) (previous answer given by expert of Lower bound= -0.028 Upper bound=2.228 Was marked incorrect) Question 2 You wish to test the following claim (Ha) at a significance level of α=0.005 Ho:p1=p2 Ha:p1>p2You obtain 19.3% successes in a sample of size n1=445 from the first population. You obtain 12.8% successes in a sample of size n2=775 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an…
A simple random sample of 95 basketball players is taken from different teams and their mean weight is found to be 226 pounds and the standard deviation of the population is 20 pounds. Using 0.05 level of significance, test the claim that the average weight for all basketball players is 231 pounds. Complete the following steps: Step # 1: Write the null hypothesis Ho [ Select ] and the alternative hypothesis H1 [ Select ] and identify the claim [Select] Step # 2: Indicate what type of test has to be used [Select ] and find the critical value(s). ( Select ] Step # 3: Find the test value. [ Select ] Step # 4: Make the decision about the null hypothesis. [ Select ] Step # 5: Summarize the result. (Select J
Question 3It is believed that the waiting time for a service has a population mean value of µ =13minutes. One wants to test whether the population mean is 13 minutes. The waiting time of a sample of 60 services is collected. The significance level alpha is set at 5%. The Excel data analysis results are presented in table 2.1) Give appropriate null and alternative hypotheses.Null hypothesis H 0 .Alternative hypothesis H 1 2) Find the p value for this test.3) What decision should be made about the hypotheses? Give evidence for your choice.Table 2: One sample t-test results VariableMean 14.72Variance 34.38Observations 60.00Hypothesized Mean 0.00 DifferenceDf 59.00t Stat 2.27P(T<=t) one-tail 0.02t Critical one-tail 1.67P(T<=t) two-tail 0.04t Critical two-tail 2.00
QUESTION 5 You want to run a 2-tailed independent t-test on sample 1 (M = 42.8, SD = 1.8) and sample 2 (M = 39.6, SD = 0.9), which each have sample size = 9. You have set a = 0.05. Assume equal variances and calculate t_obs.
A random sample is selected from a normal population with a mean of μ=50 and a standard deviation of σ=12. After a treatment is administered to the individuals in the sample, the sample mean is found to be M=55. If the sample consists of n=16 scores, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with α =0.05. If the sample consists of n=36 scores, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with α =0.05. Compare your answers for parts a and b, explain how the size of the sample influences the outcome of a hypothesis test.
Currently patrons at the library speak at an average of 65 decibels. Will this average increase after the installation of a new computer plug in station? After the plug in station was built, the librarian randomly recorded 52 people speaking at the library. Their average decibel level was 70.5 and their standard deviation was 15. What can be concluded at the the αα = 0.01 level of significance? For this study, we should use The null and alternative hypotheses would be: H0:H0: H1:H1: The test statistic = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is αα Based on this, we should the null hypothesis.
A study is to be performed to determine a certain parameter in a community. From a previous study a sd of 46 was obtained. If a sample error of up to 4 is to be accepted. How many subjects should be included in this study at 99% level of confidence?
2. Two detergents were tested for their ability to remove stains. The first one was suc- cessful on 63 out of 91 trials and the second one was successful on 42 out of 79 trials. Construct approximated 95% one-sided confidence intervals for the difference pi – P2 where the successful rates are pi and p2, respectively.
The body temperatures of two species of geckos were measured. The n = %3D 10 geckos from species A had a mean noon temperature of = 32.66°C and a standard deviation of s1 = 0.81°C, whereas the n2 = 11 geckos from species %3D B yielded mean = 30.12°C noon temperature and s2 = 0.75°. To test the %3D hypothesis of no difference versus the alternative of a difference in mean noon temperature the 5% level of significance, one would need to calculate the t-calculated value. What are thet calculated and t critical values? Calculated = 7.46; Critical = 2.776 %3D %3D Calculated = -3.458; Critical = 2.080 %3D %3D Calculated = 7.46; Critical = 2.093 Calculated = -3.458; Critical = 2.776
Suppose you measure a variable on two samples from two populations, the first of size 31 and the second of size 8. You calculate that the first sample has an average of -31 with standard deviation 2, while the second sample has an average of -35 with a standard deviation of 4. t-statistic for this experiment is 2.74. assume you are looking for any difference between the means of the two populations. You should reject or fail to reject the null hypothesis at signficance level .05? a.Impossible to determine because the p-value is equal to the significance level b. Reject c. Fail to Reject

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