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.
The difference in the Organic Chemistry final exam scores between last semester and three years ago will be analyzed by the dean. Although the standard deviations of these populations are unknown, the dean has evidence that they are equal. A sample of 41 of these scores from last semester had a mean of 63.7 and standard deviation of 4.6, and a sample of 37 scores from three years ago had a mean of 64.7 and standard deviation of 5. A claim is made that the mean final exam score from last semester ( 1) is less than the mean final exam score from three years ago (2). For each part below, enter only a numeric value in the answer box. For example, do not type "z =" or "t=" before your answers. Round each of your answers to 3 places after the decimal point. 1 (a) Calculate the value of the test statistic used in this test. Test statistic's value= (b) Use your calculator to find the P-value of this test. P-value = 0.180 F3 Submit Question 4 R F4 H % 5 T Q F5 A 6 Y F6 & 7 U F7 * PrtScn 8 F8…
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…
In the year 2033, katy perry is a leading traveling nurse. Katy is interested in reducing the mean recovery time for patients after experiencing a serious injury (assume recovery times are normally distributed). Suppose the mean recovery time is presently 8.6 months. Katy takes a random sample of 46 patients that have experienced serious injury to participate in a new treatment program and finds the sample mean is 8.1 months and a sample standard deviation of 1.2 months. Using α = 0.05, answer the following questions. g) What is the interpretation (not your conclusions) of the p value in the context of the problem you found in part e? h) What are your conclusions in the context of the problem? Relate your conclusions to the test statistic and critical value, confidence interval and p value.
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.
In the year 2033, Sarai Patterson is a leading traveling nurse. Sarai is interested in reducing the mean recovery time for patients after experiencing a serious injury (assume recovery times are normally distributed). Suppose the mean recovery time is presently 8.6 months. Sarai takes a random sample of 46 patients that have experienced serious injury to participate in a new treatment program and finds the sample mean is 8.1 months and a sample standard deviation of 1.2 months. Using α = 0.05, answer the following questions. a) What is the setup for your null and alternative hypothesis? b) What is the value of the test statistic? c) What is/are the critical value(s)?
A simple random sample of 85 basketball players is taken from different teams and their mean weight is found to be 230 pounds and the standard deviation of the population is 18 pounds. Using 0.01 level of significance, test the claim that the average weight for all basketball players is 225 pounds. Complete the following steps: Step # 1: Write the null hypothesis Ho (Select ] and the alternative hypothesis H, [ 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 ]
To study the water PH level, two independent lakes were selected for sampling. In a duration of one year, 12 samples (one in each month) are selected from each lake. water samples are taken from two different lakes. The PH mean and standard deviation of lake 1 sample were found to be 6.5 and 0.2, while the PH mean and standard deviation of lake 2 sample were found to be 7.2 and 0.1. (a) Find a 90% confidence interval for Hi – H2 (i.e., the difference between the population means for the two lakes) assuming that the populations are approximately normally distributed with equal variances. (b) You decide to decrease the above significance level from 0.1 to 0.01. Everything else is kept similar to above. Explain how your calculated confidence interval will change, and why? (i.e., will it become wider or narrower). (No need to calculate the new confidence interval)
Solve question 9, Part A, Part B and Part C only.

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