4.7 A chemist wishes to test the effect of four chemical agents on the strength of a particular type of cloth. Because there might be variability from one bolt to another, the chemist decided to use a randomized block design, with the bolts of cloth considered as blocks. She selects five bolts and applies all four chemicals in random order to each bolt. The resulting tensile strength follow. Analyze the data from this experiment (use a = 0.05) and draw appropriate conclusion. Bolt Chemical 1 4 5 1 73 68 74 71 67 2 73 67 75 72 70 3 75 68 78 73 68 4 73 71 75 75 69
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- assume that the data was obtained from two indepen-dent samples. That is, 28 subjects were enrolled into the study, and half were randomly assignedto the corn flakes diet, and half to the oat bran diet. After two weeks the LDL cholesterol level ofeach individual was recorded. LDL (mmol/l)Subject Corn Flakes Oat Bran1 4.61 3.842 6.42 5.573 5.40 5.854 4.54 4.805 3.98 3.686 3.82 2.967 5.01 4.418 4.34 3.729 3.80 3.4910 4.56 3.8411 5.35 5.2612 3.89 3.7313 2.25 1.8414 4.24 4.14 Questions; a) What are the appropriate null and alternative hypotheses for a two-sided test?(b) Conduct the test at the 0.05 level of significance. What is the p-value?(c) Construct a 95% confidence interval.Q5) An article in the ACI Materials Journal (Vol. 84, 1987, pp. 213–216) describes several experiments investigating the rodding of concrete to remove entrapped air. A 3-inch & 6-inch cylinder was used, and the number of times this rod was used is the design variable. The resulting compressive strength of the concrete specimen is the response. The data shown is posted on BruinLearn Week 2: A. Is there any difference in compressive strength due to the rodding level? Use (α= 0.05). B. Find the P-value for the F statistic in part (a). C. Analyze the residuals from this experiment. What conclusions can you draw about the underlying model assumptions? D. Construct a graphical display to compare the treatment means as described in your lecture notes.When computing the Z value to compare between two samples of two populations, o2 is a parameter of the statistical equation. Select one: O True O False
- A group of students measure the length and width of a random sample of beans. They are interested in investigating the relationship between the length and width. Their summary statistics are displayed in the table below. All units, if applicable, are millimeters. Mean width: 7.555 Stdev width: 0.914 Mean height: 12.686 Stdev height: 1.634 Correlation coefficient: 0.8203 d) If the students are interested in using the height of the beans to predict the width, calculate the slope of this new regression equation. e) Write the equation of the best-fit line that can be used to predict bean widths. Use x to represent height and y to represent width.Go through the steps of ANOVA hypothesis testing to see if you can conclude that there is a difference among population means. Let a = 0.05. Research by Singh et al. as reported in the journal Clinical Immunology and Immunopathology is concerned with immune abnormalities in autistic children. As part of their research they took measurements on the serum concentration of an antigen in three samples of children, all of whom were 10 years old or younger. The results in units per milliliter of serum follow. Autistic Children: 755, 385, 380, 215, 400, 343, 415, 360, 345, 450, 410, 435, 460, 360, 225 Normal Children: 165, 390, 290, 435, 235, 320, 330, 205, 375, 345, 305, 220, 270, 355, 360 Mentally Retarded Children: 380, 510, 315, 565, 715, 380, 390, 245, 155, 335, 295, 200, 105, 105, 245 What is the Sum of Squares between group?A car company claims that their Super Spiffy Sedan averages 31 mpg. You randomly select 8 Super Spiffies from local car dealerships and test their gas mileage under similar conditions. You get the following MPG scores: MPG: 30 28 32 26 33 25 28 30 Does the actual gas mileage for these cars deviate significantly from 31 (alpha = .05)?
- A traffic office in a country was in charge of a study where the safety of passengers in different types of cars was examined. Three models were examined; small cars, minivans and SUVS and six cars in each category were inspected. A special traffic accident simulator was used in the study and the pressure on the drivers' heads was measured. Umferðarastofa wanted to investigate whether there was a difference in the average pressure on the head during a collision in these three types of cars and used a variance analysis for this purpose. Failed to complete the square sum table, which can be seen below. weekend sum degree of freedom ave week sums between groups (area) 725.4 within groups (area) 178.6 XXX total Questions 1-3 deal with this study by the Traffic Authority. Question 1 What value should be given where xxx is in the table? 1 1.91 2. 2679 3. 3036.2 4. The information provided cannot be answered. Question 2 to be used to check if there is a difference in the average- What is the…A baseball pitcher, concerned about losing speed from his fastball, undertook a new training regimen during the offseason. His team's pitching coach measured the speed of 20 random fastballs (in miles per hour) thrown by the pitcher during spring training, and compared it with a sample of 20 random fastballs thrown during the pitcher's last five starts in the previous season. The results are shown in the following table. Assume that the pitcher's fastball speeds had a standard deviation of 2.9 miles per hour both before and after the training regimen and that the speeds for both time periods are normally distributed. Let the pitcher's fastball speeds in the previous season be the first sample, and let the pitcher's fastball speeds in spring training be the second sample. At the 0.05 level of significance, is there evidence that the pitcher is throwing fastballs at higher speeds? Find the test statistic, rounded to two decimal places, and the p-value, rounded to three decimal places.…Answer the given problem. Use the steps in hypothesis testing when presenting the results. A health researcher is interested in comparing 3 methods of weight loss: low calorie diet, low fat diet and high exercise regimen. He selected 15 moderately overweight subjects and randomly assigned 5 to each weight-loss program. The following weight reductions (in lbs) were observed after a one-month period. Test the hypothesis that the extent of weight reduction does not differ by type of weight-loss program. Low Fat : 7 7 5 4 6 Low Calorie : 7 8 8 5 High Exercise Regimen: 7 9 7 9 8 8
- Roy's Texaco wants to keep the price of its unleaded gasoline competitive with that of other stations in the area. Roy's is currently charging $1.29 per gallon. To check that the average price for this gasoline for all stations within 12-mile radius is higher than his price, Roy randomly samples the price of unleaded gasoline at ten stations located in this area. He obtains the following data for the price per gallon (in dollars): 1.7, 1.5, 2.6, 2.2, 2.4, 2.3, 2.6, 3.0, 1.4, 2.3 Set up appropriate hypotheses and test them using a significant level of .01.Roy ‘s Texaco wants to keep the price of its unleaded gasoline competitive with that of other stations in the area. Roy’s is currently charging $1.29 per gallon. To check that the average price for this gasoline for all stations within a 15 mile radius is higher than his price, Roy randomly samples the price of unleaded gasoline at ten stations located in this area. He obtains the following data for the price per gallon (in dollars): 1.7, 1.5, 2.6, 2.2, 2.4, 2.3, 2.6, 3.0, 1.4, 2.3 Set up the appropriate hypotheses and test them using a significance level of α= .05A farmer wants to test the effectiveness of a pest control method in allowing strawberry blooms to yield marketable strawberries. Out of a random sample of 100 blooms, 67 yield marketable strawberries. Specifically, he wants to test know if there is sufficient evidence that more than three-fourths of all blooms grown with this pest control method end up as marketable strawberries. The value of the statistic for this test is z=-1.85. Which of the following is the is the approximate p-value to the nearest thousandth for this test?