An experiment was carried out to compare flow rates for four different types of nozzle.
a. Sample sizes were 5, 6, 7, and 6, respectively, and calculations gave f = 3.68. State and test the relevant hypotheses using α = .01
b. Analysis of the data using a statistical computer package yielded P-value = .029. At level .01, what would you conclude, and why?
a.
State and test the hypotheses at
Answer to Problem 35SE
The test hypotheses are:
Null hypothesis:
Alternative hypothesis:
The test reveals that the flow rates for the 4 types of nozzle are not significantly different.
Explanation of Solution
Given info:
An experiment conducted to compare the flow rates for 4 types of nozzle considered respective sample sizes 5, 6, 7, 6 with F statistic value
Calculation:
Let the average flow rates for the 4 types of nozzle be
The test hypotheses are:
Null hypothesis:
That is, the flow rates for 4 types of nozzle are equal.
Alternative hypothesis:
That is, the flow rates for at least 2 types of nozzle are not equal.
The test statistic value is found to be
Degrees of freedom (df):
The number of treatments is
The total number of observations is:
Thus, the total df is:
The error df for the one factor ANOVA or the denominator df is:
Thus, the degrees of freedom are 3, 20.
Level of significance:
The given level of significance is
Bounds of the P-value:
The Table A.9, the table for “Critical Values for F Distributions” shows that the F statistic value
Thus, the lower bound of the P-value is 0.01 and the upper bound of the P-value is 0.05.
Rejection rule:
If the
Conclusion:
Here, the P-value is greater than the level of significance.
That is,
Thus, the decision is “fail to reject the null hypothesis”.
Therefore, the data do not provide sufficient evidence to conclude that the flow rates vary for at least 2 types of nozzle.
That is, the flow rates for the 4 types of nozzle are not significantly different.
b.
Give the conclusion at level 0.01, if analysis of the yielded
Answer to Problem 35SE
It can be concluded that the flow rates for the 4 types of nozzle are not significantly different.
Explanation of Solution
Calculation:
Level of significance:
The given level of significance is
P-value:
From statistical computer package, the P-value is 0.029.
Rejection rule:
If the
Conclusion:
Here, the p-value greater than the level of significance.
That is,
Thus, the decision is “fail to reject the null hypothesis”.
Therefore, the data do not provide sufficient evidence to conclude that the flow rates vary for at least 2 types of nozzle.
That is, the flow rates for the 4 types of nozzle are not significantly different.
Want to see more full solutions like this?
Chapter 10 Solutions
Probability and Stats. for Engineering.. (Looseleaf)
- An article in the Journal of Applied Polymer Science (Vol. 56, pp. 471–476, 1995) studied the effect of the mole ratio of sebacic acid on the intrinsic viscosity of copolyesters.- The data follows: Viscosity 0.45 0.2 0.34 0.58 0.7 0.57 0.55 0.44 Mole ratio 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 (a) Construct a scatter diagram of the data.arrow_forwardThe sulfate ion concentration in natural water can be determined by measuring the turbidity that results when an excess of BaCl2 is added to a measured quantity of the sample. A turbiditimeter, the instrument used for this analysis, was calibrated with a series of standard Na2SO4 solutions. The following data were obtained for the calibration:arrow_forwardAn article in the ASCE Journal of Energy Engineering [“Overview of Reservoir Release Improvements at 20 TVA Dams” (Vol. 125, April 1999, pp. 1–17)] presents data on dissolved oxygen concentrations in streams below 20 dams in the Tennessee Valley Authority system. The observations are (in milligrams per liter):arrow_forward
- Suppose a linear model y=β0+β1xy=β0+β1x is fit to a sample data set, and a test of the null hypothesis H0:β1=0H0:β1=0 against an alternative hypothesis HA:β1≠0HA:β1≠0 is performed; a PP-value of 0.4203 is obtained. Which of the following scatter plots depicts the data set on which this model was fit and the hypothesis test was performed?arrow_forwardLet ?1 denote true average tread life for a premium brand of P205/65R15 radial tire, and let ?2 denote the true average tread life for an economy brand of the same size. Test H0: ?1 − ?2 = 5000 versus Ha: ?1 − ?2 > 5000 at level 0.01, using the following data: m = 45, x = 42,100, s1 = 2400, n = 45, y = 36,200, and s2 = 1800.Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = State the conclusion in the problem context. Fail to reject H0. The data does not suggest that the difference in average tread life exceeds 5000.Reject H0. The data suggests that the difference in average tread life exceeds 5000. Fail to reject H0. The data suggests that the difference in average tread life exceeds 5000.Reject H0. The data does not suggest that the difference in average tread life exceeds 5000.arrow_forwardLet ?1 denote true average tread life for a premium brand of P205/65R15 radial tire, and let ?2 denote the true average tread life for an economy brand of the same size. Test H0: ?1 − ?2 = 5000 versus Ha: ?1 − ?2 > 5000 at level 0.01, using the following data: m = 45, x = 42,100, s1 = 2400, n = 45, y = 36,200, and s2 = 1800. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = State the conclusion in the problem context. Fail to reject H0. The data does not suggest that the difference in average tread life exceeds 5000.Reject H0. The data suggests that the difference in average tread life exceeds 5000. Fail to reject H0. The data suggests that the difference in average tread life exceeds 5000.Reject H0. The data does not suggest that the difference in average tread life exceeds 5000.arrow_forward
- If the test of H0: = 19 against Ha: ≠ 19 based on an SRS of 15 observations from a Normal populationproduces the statistic of t = –1.75. The P-value isarrow_forwardResearchers interested in lead exposure due to car exhaust sampled the blood of 52 police officers subjected to constant inhalation of automobile exhaust fumes while working traffic enforcement in a primarily urban environment. The blood samples of these officers had an average lead concentration of 124.32 µg/l and a SD of 37.74 µg/l; a previous study of individuals from a nearby suburb, with no history of exposure, found an average blood level concentration of 35 µg/l. Based on your preceding result, without performing a calculation, would a 99% confidence interval for the average blood concentration level of police officers contain 35 µg/l? Based on your preceding result, without performing a calculation, would a 99% confidence interval for this difference contain 0? Explain why or why not.arrow_forwardQ1 A) List down the measures of central tendency and measures of dispersion 2) The operations manager of a plant that manufactures tires wants to compare the actual inner diameters of two grades of tires, each of B) which is expected to be 575 millimeters. A sample of five tires of each grade was selected, and the results representing the inner diameters of the tires, ranked from smallest to largest, are as follows. Grade X grade Y 568 570 575 578 584 573 574 575 577 578 requirement. a) for each of the tow grades of tries, compute the mwan, median, and standred deviation. b) which grade of tire providing better quality? explain. c) what would be the effect on your answer in (a) and (b) if the last value for grade Y were 588 insert 578 explain. C) The file contins the overall miles per gallon (MPG) OF 2010 family sedan: 24 21 22 23 24 34 34 34 20 20 22 22 44 32 20 20 22 20 39 20 Source:…arrow_forward
- Penicillin is produced by the Penicillin fungus, which is grown in a broth whose sugar content must be carefully controlled. Several samples of broth were taken on three successive days, and the amount of dissolved sugars, in milligrams per milliliter, was measured on each sample. The results were as follows. Day 1 : 4.9 5.4 5.3 4.9 5.2 5.1 5.4 4.9 5.1 5.1 4.9 5.4 Day 2 : 5.5 5.2 5.1 5.0 5.3 5.4 5.3 5.2 5.4 5.3 5.4 5.1 Day 3 : 5.8 5.0 5.4 5.5 5.5 5.5 4.8 5.5 5.2 4.9 5.5 5.0 Construct an ANOVA table. Round your answers to four decimal places as needed. One-way ANOVA: Sugar Concentration Source DF SS MS F P Days Error Total Is there enough evidence to conclude that the mean sugar concentration…arrow_forwardUse the following data to determine if drug B produces higher creatinine levels than drug A, assume the data is normally distributed. Creatinine levels (µmol/L) Drug A Drug B 48.2 52.3 54.6 57.4 58.3 55.6 47.8 53.2 51.4 61.3 52.0 58.0 55.2 59.8 49.1 54.8 49.9 52.6 Write out the null and alternative hypothesis in *words and symbols*. What is the hypothesis in words? Determine the critical value (use a significance level of 0.05) Calculate the test statistic, and determine if the results are significant or not. How did you calculate the standard deviations? Please provide a complete outline of calculationsarrow_forwardThe following data are from a repeated-measures experiment comparing three different treatment conditions. Participant Treatment A Treatment B Treatment C A 0 1 2 B 2 5 5 C 1 2 6 D 5 4 9 E 2 8 8 TA= 10 TB= 20 TC= 30 G= 60 SSA= 14 SSB= 30 SSc= 30 SStotal=370 Conduct a repeated measures ANOVA with alpha =.05 to determine whether there are any difference between the means. Show work for all intermediary steps and include a source table for the ANOVA and calculate the partial η2 for the effect of treatment on scores. conduct any post hoc tests to determine mean differences (if the ANOVA is significant). Set up a dataset on SPSS with data from the last problem. Calculate the ANOVA and partial η2 and report the F statistic in APA format: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