placed under a known load (force). Smaller beams made of the same material will then be used as springs to protect electronics. The manufacturer needs the beam to flex on average 5.0 mm, with 95 % of all samples having a flex between 4.7 mm and 5.3 mm. After testing the flex of 20 samples, the following numbers are found: 20 i=1 x₁ = 102.2 mm 20 i=1 2 Xi = 523.7 mm² Each sample has the flex measured to the nearest 0.1 mm using electronic calipers. What is the mean flex found using 20 samples? What is the sample standard deviation of flex found using 20 samples?
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- The "spring-like effect" in a golf club could be determined by measuring the coefficient of restitution (the ratio of the outbound velocity to the inbound velocity of a golf ball fired at the clubhead). Twelve randomly selected drivers produced by two clubmakers are tested and the coefficient of restitution measured. The data follow: Club 1: 0.8406, 0.8104, 0.8234, 0.8198, 0.8235, 0.8562, 0.8123, 0.7976, 0.8184, 0.8265, 0.7773, 0.7871 Club 2: 0.8305, 0.7905, 0.8352, 0.8380, 0.8145, 0.8465, 0.8244, 0.8014, 0.8309, 0.8405, 0.8256, 0.8476 Test the hypothesis that both brands of ball have equal mean overall distance. Use α = 0.05 and assume equal variances. Question: Reject H0 if t0 < ___ or if t0 > ___.A researcher wonders whether younger mothers have babies that are significantly heavier or lighter than the population average of μ 7.25 pounds. The researcher collects data from N = 35 babies who were born to mothers between the ages of 16 and 18. The average weight for these babies was M = 7.15 pounds (SD = .6 pounds).One operation of a mill is to cut pieces of steel into parts that will later be used as the frame for front seats in an automobile. The steel is cut with a diamond saw and requires the resulting parts to be within 10.005 inch of the length specified by the automobile company. Data are collected from a sample of 50 steel parts and are shown in the following table. The measurement reported is the difference in inches between the actual length of the steel part, as measured by a laser measurement device, and the specified length of the steel part. For example, the first value, -0.003, represents a steel part that is 0.003 inch shorter than the specified length. Complete parts a through c Click the icon to view the data table. a. Construct a frequency distribution Difference in Length -0.005 but less than -0.003: -0.003but less than -0.001 -0.001but less than 0.001 0.001but less than 0.003 0.003but less than 0.005 Frequency Difference Between Actual and Specified Lengths 0.002 0 -0.003…
- An education researcher claims that 60% of college students work year-round. In a random sample of 200 college students, 120 say they work year-round. At a = 0.10, is there enough evidence to reject the researcher's claim? Complete parts (a) through (e) below.How heavy a load (pounds) is needed to pull apart pieces of Douglas fir 4 inches long and 1.5 inches square? Students doing a laboratory exercise sample 20 pieces of wood and find an average load capacity of 30,841 pounds. We are willing to regard the wood pieces prepared for the lab session as an SRS of all similar pieces of Douglas fir. Engineers also commonly assume the characteristics of materials vary normally. Suppose that the strength of pieces of wood like these follow a normal distribution with a population standard deviation of 3,000 pounds (As you can see all three necessary assumptions are met). a. Assuming that all evergreen wood has a known "load" capacity average of 30,000 pounds. Make a two-sided hypothesis (null and alternative statement) about Douglas Fir "load" capacity compared to the overall average. b. Apply the formula for finding our test statistic (show your work or describe the process) Specifically, use the formula for the z-statistic (pasted below and on…The specification for the pull strength of a wire that connects an integrated circuit to its frame is 10 g or more. Units made with aluminum wire have a defect rate of 10%. A redesigned manufacturing process, involving the use of gold wire, is being investigated. The goal is to reduce the rate of defects to 5% or less. Out of the first 100 units manufactured with gold wire, only 4 are defective. True or false: a) Since only 4% of the 100 units were defective, we can conclude that the goal has been reached. b) Although the sample percentage is under 5%, this may represent sampling variation, so the goal may not yet be reached. c) There is no use in testing the new process, because no matter what the result is, it could just be due to sampling variation. d) If we sample a large enough number of units, and if the percentage of defective units is far enough below 5%, then it is reasonable to conclude that the goal has been reached.
- Everest auto industry produces bearing for Mahindra Motor Corporation. The precision of radius of bearing is very important for its successful functioning. To check the variability in the bearing radius, the company randomly selected ten bearings and measured the radius, the result of which is as shown in the table below. #no Nominal radius (cm) #no Nominal radius (cm) 1 2.70 6 2.59 2 2.65 7 2.73 3 2.75 8 2.64 4 2.55 9 2.88 5 2.76 10 2.83 Calculate the sample standard deviation for the above data. Construct a box plot and check whether there is any outlier data in the data distribution. Based on the comparison between the mean and the quartile, identify the shape of the data distribution. Calculate the 65th percentile and interpret the result. What is the range of the data distribution? Explain its meaning.To illustrate the effects of driving under the influence (DUI) of alcohol, a police officer brought a DUI simulator to a local high school. Student reaction time in an emergency was measured with unimpaired vision and also while wearing a pair of special goggles to simulate the effects of alcohol on vision. For a random sample of nine teenagers, the time (in seconds) required to bring the vehicle to a stop from a speed of 60 milos per hour was recorded. Complete parts (a) and (b). Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers. E Click the icon to view the data table. (a) Whether the student had unimpaired vision or st was randomly selected. Why is this a good idea in designing the experiment? O A. This is a good idea in designing the experiment because reaction times are different O B. This is a good idea in designing the experiment because the sample size is not large enough. O C. This is a…ONLY THE LAST ONE Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type. 5.9 7.2 7.3 6.3 8.1 6.8 7.0 7.5 6.8 6.5 7.0 6.3 7.9 9.0 8.4 8.7 7.8 9.7 7.4 7.7 9.7 8.2 7.7 11.6 11.3 11.8 10.7 The data below give accompanying strength observations for cylinders. 6.5 5.8 7.8 7.1 7.2 9.2 6.6 8.3 7.0 8.3 7.8 8.1 7.4 8.5 8.9 9.8 9.7 14.1 12.6 11.9 Prior to obtaining data, denote the beam strengths by X1, . . . , Xm and the cylinder strengths by Y1, . . . , Yn. Suppose that the Xi's constitute a random sample from a distribution with mean μ1 and standard deviation σ1 and that the Yi's form a random sample (independent of the Xi's) from another distribution with mean μ2 and standard deviation σ2. (a) Use rules of expected value to show that X − Y is an unbiased estimator of μ1 − μ2. E(X − Y) = E(X) − E(Y) = μ1 − μ2 E(X − Y) = E(X) − E(Y) 2 = μ1 − μ2 E(X − Y) = nm E(X) − E(Y) = μ1 − μ2 E(X −…
- An alloy manufacturer is investigating if they can improve the strength of one of their alloysby producing it at a lower temperature. To investigate that, they produce the alloy at twodifferent temperatures (high and low) and then measure the breaking strength of randomsamples of specimens from each. The following table represents the strength of the randomsamples at the higher and lower temperature, in units of 0.001-inch deflection. Temp. Strength (0.001 inch)High 87 64 66 85 76 49 97 73 75 77 69 68 89 27 58 84Low 88 82 81 85 79 80 88 78 77 85 79 76 Do the results support the hypothesis that lowering the production temperature can improve thestrength of the alloy, with 95% confidence? (Hint: Don’t forget investigating variances. Use 98% confidence for that.)Naini, Cobourne, McDonald and Donaldson (2008) reported that a specific ratio of height to face length of 1 to 8.5 tended to be rated as most attractive—almost exactly what Da Vinci’s idealized Vitruvian Man, predicts as “perfection” in the human form. For this study, we want to see if there is a relationship between a person’s height and head circumference. We get a random sample of 40 people and measure both their height and their head size to the nearest centimeter. What test should you use and why?A medical researcher says that less than 82% of adults in a certain country think that healthy children should be required to be vaccinated. In a random sample of 300 adults in that country, 78% thínk that healthy children should be reguired to be vaccinated. At a = 0.10, is there enough evidence to support the researcher's claim? Complete parts (a) through (e) below. H: ps O E. Ho: p= Hyip Haip= O D. Ho: p. O B. The rejection region is I test statisticz Fail to reject laces as needed.) Reject ject or fail to reject the null hypothesis and (e) interpret the decision in the context of the original claim. the null hypothesis. There V enough evidence to V the researcher's claim.