Two machines are used for filling glass bottles with a soft-drink beverage. The filling processes have known standard deviations al σ1 = 0.010 liter and σ2 = 0.015 liter, respectively. A random sample of n1 = 25 bottles from machine 1 and n2 = 20 bottles from machine 2 results in average net contents of
- (a) Test the hypothesis that both machines fill to the same net contents, using α = 0.05. What are your conclusions?
- (b) Find the P-value for this test.
- (c) Construct a 95% confidence interval on the difference in
mean fill volume.
Want to see the full answer?
Check out a sample textbook solutionChapter 4 Solutions
Introduction to Statistical Quality Control
Additional Math Textbook Solutions
Elementary Statistics Using The Ti-83/84 Plus Calculator, Books A La Carte Edition (5th Edition)
Statistics: Informed Decisions Using Data (5th Edition)
Essentials of Statistics, Books a la Carte Edition (5th Edition)
Business Statistics: A First Course (7th Edition)
Basic Business Statistics, Student Value Edition
- Two independent samples of respective sizes 6 and 8, respective means 78 and 96, and respective standard deviations 3 and 9, were selected from two normal populations with equal variances. Need to test the null hypothesis that the two population means are equal versus they are different. Based on these two samples, we can conclude the following about this test at α = 0.05 a. the value of the test statistic is 2.5205 and the the cut-off value is 2.201 , so we reject H0 b. the value of the test statistic is 2.49971 and the the cut-off value is 1.64 , so we accept H0 c. None of these d. the value of the test statistic is 2.49971 and the the cut-off value is 1.28 , so we reject H0 e. the value of the test statistic is 2.5205 and the the cut-off value is 1.782 , so we accept H0arrow_forwardTwo distinct solid fuel propellants, type A and type B, are being considered for a space program activity. Burning rates of the propellant are crucial. Random samples of 26 specimens of the two propellants are taken with sample means 20.1 cm/sec for propellant A and 24.1 cm/sec for propellant B. It is generally assumed that the variability in burning rate is roughly the same for the two propellants and is given by a population standard deviation of 5 cm/sec. Assume that the burning rates for each propellant are approximately normal and hence make use of the Central Limit Theorem. Nothing is known about the two population mean burning rates, and it is hoped that this experiment might shed some light on them. Complete parts (a) and (b) below. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) If, indeed, µÃ = µÂ, what is P(XB-XA 24.0)? P(XB-XA24.0) = (Round to four decimal places as needed.) werarrow_forwardTwo independent samples of respective sizes 12 and 11, respective means 99 and I13, and respective standard deviations 10 and 6, were selected from two normal populations with equal variances. Need to test the null hypothesis that the two population means are equal versus they are different. Based on these two samples, we can conclude the following about this test at a = 0.1 O a. the value of the test statistic is 1.67904 and the the cut-off value is 1.725, so we accept HO O b. the value of the test statistic is 1.67904 and the the cut-off value is 1.323, so we reject HO O C. None of these O'd. the value of the test statistic is 2.11826 and the the cut-off value is 1.64, so we reject HO O e. the value of the test statistic is 2.11826 and the the cut-off value is 1.28, so we accept HOarrow_forward
- A grocery store receives deliveries of corn from two farms, one in Iowa and the other in Ohio. Both farms produce ears of corn with mean weight 1.26 pounds. The standard deviation of the weights of the ears of corn from the farm in Ohio is 0.01 pound greater than that from the farm in Iowa. A randomly selected ear of corn from the farm in Iowa weighed 1.39 pounds, which has a standardized score of 1.645 for the distribution of weights for the Iowa corn. If an ear of corn from the farm in Ohio weighs 1.39 pounds, how many standard deviations from the mean is the weight with respect to the Ohio distribution?arrow_forwardVolunteers who had developed a cold within the previous 24 hours were randomized to take either zinc or placebo lozenges every 2 to 3 hours until their cold symptoms were gone. Twenty-five participants took zinc lozenges, and 23 participants took placebo lozenges. The mean overall duration of symptoms for the zinc lozenge group was x, = 4.4 days, and the standard deviation of overall duration of symptoms was 1.4 days. For the placebo group, the mean overall duration of symptoms was x, = 7.9 days, and the standard deviation was 1.6 days. (a) Calculate x, - x, difference in sample means and also compute the unpooled s.e.(x, - x,) standard error of the difference in means. (Round all answers to the nearest hundredth.) X2 - X1 s.e.(x2 - x,) = | days days (b) Compute a 95% confidence interval for the difference in mean days of overall symptoms for the placebo and zinc lozenge treatments. Use the unpooled standard error and use the smaller of n, - 1 and n, - 1 as a conservative estimate of…arrow_forwardTwo independent samples of respective sizes 12 and 11, respective means 99 and 113, and respective standard deviations 10 and 6, were selected from two normal populations with equal variances. Need to test the null hypothesis that the two population means are equal versus they are different. Based on these two samples, we can conclude the following about this test at a = 0.1 O a. the value of the test statistic is 1.67904 and the the cut-off value is 1.725, so we accept HO O b. the value of the test statistic is 2.11826 and the the cut-off value is 1.28 , so we accept HC O c. the value of the test statistic is 2.11826 and the the cut-off value is 1.64 , so we reject HO O d. None of these O e. the value of the test statistic is 1.67904 and the the cut-off value is 1.323 , so we reject H0arrow_forward
- In a study of carbohydrate diet, an investigator wishes to test a hypothesis test for whether the population mean of cholesterol level among individuals taking medium carbohydrate diet for 4 months is different than 7.8 mmol/L A simple random sample (SRS) of 30 study participants is conducted. Subjects are randomized to receive medium carbohydrate diet for 4 months. The total cholesterol level at the time of entering the study had an average of 5.20 mmol/L and standard deviation of 1.3 mmol/L Calculate a 95% confidence interval (show your work) for the population mean of total cholesterol levels among those taking medium carbohydrate diet and use the confidence interval to draw a conclusion as to whether there is a difference in cholesterol levels. Choose the correct statement. O (4.7492, 5.6508) Do not reject HO sincc value of null hypothesis, 5.20 does fall in this range O (4.8216. 5.5783) Reject H0 since value of null hypothesis 7.8 does not fall in this range. O 14.7492. 5.6508)…arrow_forwardA researcher compares two compounds (1 and 2) used in the manufacture of car tires that are designed to reduce braking distances for SUVs equipped with the tires. SUVs equipped with tires using compound 1 have a mean braking distance of 7777 feet and a standard deviation of 12.812.8 feet. SUVs equipped with tires using compound 2 have a mean braking distance of 8585 feet and a standard deviation of 5.35.3 feet. Suppose that a sample of 3333 braking tests are performed for each compound. Using these results, test the claim that the braking distance for SUVs equipped with tires using compound 1 is shorter than the braking distance when compound 2 is used. Let μ1μ1 be the true mean braking distance corresponding to compound 1 and μ2μ2 be the true mean braking distance corresponding to compound 2. Use the 0.10.1 level of significance. Step 1 of 4 : State the null and alternative hypotheses for the test.arrow_forwardTwo different formulations of an oxygenated motor fuel are being tested to study their road octane numbers. The variance of road octane number for formulation 1 is o? = 2.2 and for formulation 2 it is o = 1.8. Two random samples of size n = 42 and %3D n2 = 45 are tested, and the mean road octane numbers observed %3D are X = 89.6 and X, = 92.5. Assume the samples are random and independent from a normal population. Construct an 80% two-sided confidence interval on the difference in mean road octane number. < 1 - H2<arrow_forward
- The Batteries sheet of the Data Excel file shows the results of two random samples that measured the average number of minutes per charge for AA Lithium-ion (Li-ion) rechargeable batteries versus Nickel-Metal Hydride (NiMH) rechargeable batteries. Perform a hypothesis test using significance level (α) = 0.05 to determine if the true average number of minutes per charge for NiMH batteries is smaller than that for Li-ion batteries. Let:µLi-ion be the true average number of minutes per charge for Li-ion batteries µNiMH be the true average number of minutes per charge for NiMH batteries. t-Test: Two-Sample Assuming Unequal Variances NiMH Li-ion Mean 89.35714 95 Variance 3.93956 59.75 Observations 14 17 Hypothesized Mean Difference 0 df 19 t Stat -2.89621 P(T<=t) one-tail 0.004628 t Critical one-tail 1.729133 P(T<=t) two-tail 0.009255 t Critical two-tail 2.093024 Based on the…arrow_forwardA researcher is interested in studying the average number of traffic violations received by male vs. female drivers. The researcher has a sample of 30 male drivers and 32 female drivers and conducts a two-sample t-test (two-tailed, alpha = .05). The researcher finds the following: 1. Male drivers have an average of 4 traffic violations every year. 2. Female drivers have an average of 2 traffic violations every year. 3. The standard error of the mean difference between male and female drivers (i.e., the se) is .50. What are the degrees of freedom for this test? Enter your answer as a whole number with no decimal places (i.e., 10, not 10.01, not 10.0, not 10.1).arrow_forwardThere are many different properties of wood, for example, thermal conductivity, vapor permeance and air permeability. The dry density of wood is often used as a measure of shear strength. A study was conducted to compare the strengths of oriented strand board (OSB) and plywood. Independent random samples of each type of wood were obtained and the dry density of wood (in kg/m3) was measured. (i) Assuming that the population standard deviations of the two groups are the same, test, at the 2% level of significance, whether the dry density of OSB is different to that of plywood. A. Use graphs (see photos) to produce the information to perform the hypothesis test in part (i). B. Is the normality requirement satisfied for the test in part (i)? Explain C. For the test in part (i), how many degrees of freedom does the distribution of the test statistic have? D. What is the value of the observed test statistic associated with the test in part (i)? E. What is the p-value associated with the…arrow_forward
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman