Our research group is developing a chemically treated natural fiber for its tensile- strength properties. Twenty-five pieces were tested under similar conditions and the results showed an average tensile strength of 500.05 MPa and a standard deviation of 80.55 MPa. Give the lower 99 % prediction interval on a single observed tensile strength value in MPa. O 280.6 O 289.95 O 290.25 295.33
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- Over the past 10 years, contestants at the county fair hotdog eating contest averaged 125 hotdogs within the 1 minute time frame. Due to Covid19 restrictions, there were only 15 contestants who ate an average of 122 hotdogs. s=6.5 We're interested in finding out if there is significant change in hotdog eating. Use the hypothesis that H0: µ=125, Ha: #125. What is the SE? 10.9 1.7 6.5 8.3An experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in x = 18.11 kgf/cm² for the modified mortar (m = 42) and y = 16.82 kgf/cm² for the unmodified mortar (n = 30). Let μ₁ and μ₂ be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal. (a) Assuming that ₁ = 1.6 and ₂ = 1.3, test Ho: ₁ - ₂ = 0 versus H₂ : ₁ - ₂ > 0 at level 0.01. 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. O Reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds 0. O Fail to reject Ho. The data does not suggest that the difference in average tension bond strengths…A drug manufacturer forms tablets by compressing a granular material that contains the active ingredient and various fillers. The hardness of a sample from each batch of tablets produced is measured to control the compression process. The target value for 11.5. The hardness data for a random sample of 20 tablets from one large batch are given. the hardness is Н 11.627 11.374 11.383 11.477 = 11.613 11.592 11.715 11.570 A hypothesis test of Ho: μ = 11.2 Ha: μ # 11.2 11.493 11.458 11.485 11.623 11.602 11.552 11.509 11.472 11.360 11.463 11.429 11.531 where μ = the true mean hardness of the tablets using a = 0.05 has a P-value of 0.4494. Because the P-value of 0.4494 > a = = 0.05, we fail to reject Ho. We do not have convincing evidence that the true mean hardness of these tablets is different from 11.5. A 95% confidence interval for the true mean hardness measurement for this type of pill is (11.472, 11.561). Which is the following statements is not true with regards to the 95% confidence…
- An experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in x = 18.11 kgf/cm² for the modified mortar (m = 42) and y = 16.82 kgf/cm² for the unmodified mortar (n = 32). Let μ₁ and μ₂ be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal. (a) Assuming that 0₁ = 1.6 and ₂ = 1.3, test Ho: ₁ - ₂ = 0 versus H₂: M₁-M₂ > 0 at level 0.01. 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. O Reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds 0. O Fail to reject Ho. The data suggests that the difference in average tension bond strengths exceeds…An article includes the accompanying data on compression strength (lb) for a sample of 12-oz aluminum cans filled with strawberry drink and another sample filled with cola. Sample Sample Size Mean 15 15 Beverage Strawberry Drink Cola 0.05.) Does the data suggest that the extra carbonation of cola results in a higher average compression strength? Base your answer on a P-value. (Use a = USE SALT но: H1 - H2=0 Ha: H1 -H2 0 Sample SD 22 15 P-value = H₂ for the cola.) Calculate the test statistic and determine the P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.)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).
- An experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in x = 18.18 kgf/cm2 for the modified mortar (m = 42) and y = 16.86 kgf/cm for the unmodified mortar (n = 30). Let µ1 and Hz be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal. (a) Assuming that o1 = 1.6 and o2 = 1.3, test Ho: µ1 - 42 = 0 versus H3: µ1 – 42 > 0 at level 0.01. 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 Ho: The data does not suggest that the difference in average tension bond strengths exceeds from 0. o Reject Ho: The data does not suggest that the difference in average tension bond…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 > ___.b) Civil engineers have developed a 3D model to predict the response of jointed concrete pavements to temperature variations. To check this model, they measured the change in traverse strain on six different occasions and compared this to the modelled values. The table below was obtained. Date Jul 25 Aug 4 Aug 16 - p-value, -58 69 35 Sep 3 -32 Oct 26 -40 Nov 3 -83 - conclusion, Percent Use the Summary output below to answer the following question Summary Output 4.4 (iii) Test whether the differences between the measurements are normally distributed. State your: - hypothesis, Ho Data are normally distributed HA Data are not normally distributed : - the test statistic, 99 - Decision (Reject, Retain), 95 90 80 70 60 50 40 30 20 Change in Strain Note for conclusion: -(if you think there is significant evidence data is normally distributed, enter 1) -(if you think there is significant evidence data is not normally distributed, enter O), Summary Output 4.4: 10 Field Measurement 5 1 -40…
- A new process for producing synthetic diamonds can be operated at a profitable level only if the average weight of the diamonds is greater than 0.5 karat. To evaluate the profitability of the process, six diamonds are generated, with recorded weights 0.46, 0.61, 0.52, 0.48, 0.57 and o.54 karat. Do the six measurements present sufficient evidence to indicate that the average weight of the diamonds produced by the process is in excess of 0.5 karat? Use 5% level of significanceAn engineer wants to compare the tensile strengths of steel bars that are produced using a conventional method and an experimental method. (The tensile strength of a metal is a measure of its ability to resist tearing when pulled lengthwise.) To do so, the engineer randomly selects steel bars that are manufactured using each method and records the following tensile strengths (in Newtons per square millimeter). At α=.10, can the engineer claim that the experimental method produces steel with greater mean tensile strength? Should the engineer recommend using the experimental method? First use the F test to determine whether or not to use equal variances in choosing the model.(??? ????? ?? ???? ?̅ ??? ? ??? ???ℎ ???ℎ??) Experimental 395 389 421 394 407 411 389 402 422 416 402 408 400 386 411 405 389 Conventional 362 352 380…A manufacturer of college textbooks is interested in estimating the strength of the bindings produced by a particular binding machine. Strength can be measured by recording the force required to pull the pages from the binding. If this force is measured in pounds, how many books should be tested in order to estimate with 95% confidence to within 0.1 lb the average force required to break the binding? Assume that is known to be .8 lb.