Example 22.1 A company is engaged in the manufacture of battery cells in its plant. The process is said to be under control if the mean life of battery cells is 1,200 hrs with a standard deviation of 75 hrs. Considering these values to be the process average and process dispersion, you are required to deter- mine the 3-sigma control limits for x-chart for samples of size 16.
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- Question 1: The sales representative for a manufacturer of a new product claims that the product will increase output per machine by at least 29 units per hour. A line manager installs the product on 30 of the machines, and finds that the average increase was only 26 with a standard deviation of 6.2. Using a 5% significance level, which of the following statements is true? Reject H0 if t statistic < -1.699 Reject H0 if t statistic > -1.711 Reject H0 if t statistic < -1.761 Reject H0 if t statistic < -2.16 Question 2: What is the critical value for an upper‐tailed hypothesis test of the population mean when the population variance is unknown in which a null hypothesis is tested at the 0.10 level of significance based on a sample size of 19? 1.645 1.328 1.734 1.740 Question 3 A two-tailed test is performed at 95% confidence. The p-value is determined to be 0.0478. The null hypothesis must be…Question 12 Consider this scenario: A cereal-packing company where the content of cereal boxes must have a mean of 368 grams to satisfy the labeling on the box. Because it is expensive to weigh every box produced at the factory, a sample of boxes is used to estimate the actual mean. After analyzing the data sample, the operations manager must decide whether or not the manufacturing process is working as expected. Suppose a sample of 49 boxes is taken from thousands produced during an 8-hour shift and the standard deviation (σ) of the cereal-filling process is 15, what is the standard error of the mean? Use the equation, σX̅ = σ /(square-root of n), where n is the sample size. Enter your result as a value with one digit after the decimal point (e.g. 1.7).Question 21 A quality-assurance inspector periodically examines the output of a machine to determine whether it is properly adjusted. When set properly, the machine produces nails having a mean length of 2.000 inches, with a standard deviation of 0.070 inches. For a sample of 35 nails, the mean length is 2.025 inches. If the null and alternative hypotheses can be used to conclude that the machine is adjusted properly, at 15% level of significance, do you reject or fail reject H0? Reject H0 because Z-statistic is greater than z-critical Reject H0 because Z-critical is more than 1.435 Reject H0 because Z-critical is less than -1.435 Reject H0 because Z-critical lies between 1.435 and -1.435
- Question 2 The time for an older machine to do a quality check on a newly manufactured tire,X1, has mean of 65 seconds and variance 16, while the time for a newer model, X2, has mean 45 seconds and variance 9. Find the expected time savings using the newer model whena) checking a single tire;b) checking 200 tires.c) Find the standard deviation in parts a) and b), assuming all the checking times areindependent.QUESTION #4 (12 marks) A researcher in interested in whether people can identify emotions correctly when they are extremely tired. It is known that, using a particular method of measurement, accuracy ratings of people in the general population (who are not extremely tired) are normally distributed with a mean of 82 and a variance of 20. In the present study, however, the researcher arranged to test 50 people who had no sleep the previous night and predicted they would be less accurate at identifying emotions correctly. The mean accuracy for these 50 individuals was 78. Using an alpha of 0.05, what should the researcher conclude?Question 18 A quality-assurance inspector periodically examines the output of a machine to determine whether it is properly adjusted. When set properly, the machine produces nails having a mean length of 2.000 inches, with a standard deviation of 0.070 inches. For a sample of 35 nails, the mean length is 2.025 inches. If the null and alternative hypotheses can be used to conclude that the machine is adjusted properly, at 15% level of significance, what is your conclusion? There is enough evidence to support the claim There is no enough evidence to support the claim There is enough evidence to reject the claim There is no enough evidence to reject the claim
- QUESTION 4 A. The department of labor in a state wanted to find the compensation of hotel employees. A random sample of 20 cleaning persons produced the mean hourly earnings of $10.60 with a standard deviation of $1.05. A random sample of 25 bellhops gave the mean hourly earnings of $11.20 with a standard deviation of $1.30. Assume that the hourly earnings of both groups are normally distributed with unequal unknown population variances. Using the 10% significance level, can you conclude that the mean hourly earnings of both groups are not the same in this state? Note: No need excel formulaThe median pH level of the rain in a certain county, was 4.90. A biologist obtains a random sample of 19 rain dates and obtains the following data. Test the hypothesis that the median pH level has decreased from 4.90 at the alpha= 0.05 level of significance.A researcher conducts a two-year study comparing the number of cavities in a group of 30 randomly selected young children from the community before and after the application of fluoride to test if there is a decrease in the number of cavities. This is an example of a/an: Independent-samples t test or Dependent-samples t test?
- Statewide, social workers have an average annual salary of $29,000. A random sample of 159 social workers in Pocatello have an annual salary of $29,501, with a standard deviation of $977. Are the annual salaries of social workers in Pocatello significantly different from the statewide average? Please complete all five steps of the five step model, showing as much of your work as possible. (alpha = .05 and Z(critical)+-1.96).Question # 19. With individual lines at its various windows, a post office finds that the standard deviation for waiting times for customers on Friday afternoon is 7.2 minutes. The post office experiments with a single, main waiting line and finds that for a random sample of 25 customers, the waiting times for customers have a standard deviation of 3.5 minutes on a Friday afternoon. With a significance level of 5%, test the claim that a single line causes lower variation among waiting times for customersQUESTION 4 PART A- What is the standard error of the correlation coefficient for the association of extroversion and neuroticism in personalities? QUESTION 4 PART B- Carry out a formal t-test for the association between extroversion and neuroticism in personalities.xls. H0: The population correlation coefficient is 0. HA: The population correlation coefficient is not 0. What is the value of the t-statistic corresponding to this test? (Report the absolute value. The t-distribution is symmetric, thus it is easier to compare the absolute value of the t-statistic with the positive values in statistical table C). DATA IS ATTACHED.