5. A civil engineering firm is conducting a study on the compressive strength of a new type ofconcrete mix designed for rapid construction projects. A random sample of 30 specimens of thenew concrete mix is tested for compressive strength after curing for 28 days. The sample has anaverage compressive strength of 35 MPa (megapascals) with a standard deviation of 5 MPa.a. Calculate 90% confidence interval (CI) for the population mean μ. Write down yourinterpretation.b. Calculate 95% CI for the population mean μ. Write down your interpretation.c. Calculate 99% CI for the population mean u. Write down your interpretation.d. Explain why the size of CI changed between parts a - c.Assume the compressive strength of concrete specimens follows a normal distribution.

Let X be the compressive strength of the concrete specimen.The sample mean and sample standard…

Answered: 5. A civil engineering firm is…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.3: Special Probability Density Functions

Problem 30E

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Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and inexpensive to manufacture. However, their nondegradable nature has prompted development of environmentally friendly composites using natural materials. An article reported that for a sample of 10 specimens with 2% fiber content, the sample mean tensile strength (MPa) was 51.1 and the sample standard deviation was 1.3. Suppose the true average strength for 0% fibers (pure cellulose) is known to be 48 MPa. Does the data provide compelling evidence for concluding that true average strength for the WSF/cellulose composite exceeds this value? (Use α = 0.05.) USE SALT State the appropriate hypotheses. ⒸHO: μ> 48 H₂: μ = 48 Ho: μ 48 Ho: μ = 48 H₂: μ = 48 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t = P-value = What can you conclude? O The data provides compelling…
Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and inexpensive to manufacture. However, their nondegradable nature has prompted development of environmentally friendly composites using natural materials. An article reported that for a sample of 10 specimens with 2% fiber content, the sample mean tensile strength (MPa) was 51.8 and the sample standard deviation was 1.5. Suppose the true average strength for 0% fibers (pure cellulose) is known to be 48 MPa. Does the data provide compelling evidence for concluding that true average strength for the WSF/cellulose composite exceeds this value? (Use a = 0.05.) n USE SALT State the appropriate hypotheses. Ho:H = 48 Ha:µ > 48 = 48 Hạ: u + 48 Ho: H = 48 Hai u 48 H: µ = 48 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t = P-value = What can you conclude? O The data…
Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and inexpensive to manufacture. However, their nondegradable nature has prompted development of environmentally friendly composites using natural materials. An article reported that for a sample of 10 specimens with 2% fiber content, the sample mean tensile strength (MPa) was 51.4 and the sample standard deviation was 1.5. Suppose the true average strength for 0% fibers (pure cellulose) is known to be 48 MPa. Does the data provide compelling evidence for concluding that true average strength for the WSF/cellulose composite exceeds this value? (Use α = 0.05.) Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t = P-value =
Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and inexpensive to manufacture. However, their nondegradable nature has prompted development of environmentally friendly composites using natural materials. An article reported that for a sample of 10 specimens with 2% fiber content, the sample mean tensile strength (MPa) was 51.3 and the sample standard deviation was 1.4. Suppose the true average strength for 0% fibers (pure cellulose) is known to be 48 MPa. Does the data provide compelling evidence for concluding that true average strength for the WSF/cellulose composite exceeds this value? (Use α = 0.05.) State the appropriate hypotheses. ⒸH₂: μ = 48 Ha: > 48 Ho:μ = 48 H₂H 48 H₂: μ = 48 Ho: μ< 48 H₂₁:μ = 48 USE SALT Ho: M = 48 H₂:48 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t= 7.68 X P-value =
Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and inexpensive to manufacture. However, their nondegradable nature has prompted development of environmentally friendly composites using natural materials. An article reported that for a sample of 10 specimens with 2% fiber content, the sample mean tensile strength (MPa) was 51.4 and the sample standard deviation was 1.2. Suppose the true average strength for 0% fibers (pure cellulose) is known to be 48 MPa. Does the data provide compelling evidence for concluding that true average strength for the WSF/cellulose composite exceeds this value? (Use a = 0.05.) State the appropriate hypotheses. O H,: H 48 H:u = 48 O H,: = 48 Hi u 48 OH:= 48 H: u + 48 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) P-value = What can you conclude? O The data provides compelling…
The floor has been improved to increase the strength of a floor.Average compressive strength of 80 samples before improvement was 32 kg / cm2 and standard deviation was 5.1 kg / cm2;The average compressive strength of the 95 samples after treatment is 38 kg / cm2 and the standard deviation is 6.3 kg / cm2.Determine if the improvement affects the strength of the soil in terms of mean and standard deviation at the 3% significance level.
The tensile strength of paper using 5% hardwood and 10% hardwood are to be compared. A random sample of 41 sheets made from 5% hardwood had an average tensile strength of 1.52 lbs. with a standard deviation of 0.33 lbs. A random sample of 61 sheets made from 10% hardwood had an average tensile strength of 1.88 lbs. with a standard deviation of 0.42 lbs. Can we conclude the average tensile strength is the same for the two types of paper? Use 5% significance and p-values. Part 1) Conduct the test using the assumption that the sample standard deviations are the same as the population standard deviations. Part 2) Conduct the test using the assumption that the population standard deviations are unknown but equal (you also must assume a normal population here). Part 3) Conduct the test with only the assumption that we have simple random samples from normal populations. May you please explain which stat test you used on your calculator and why. Thank you very much for your help!
The price paid for a new phone of a particular model follows a Normal distribution with mean μ=750 and standard deviation σ= 42. What proportion of these phones are purchased for more than 821 dollars? Give your answer to four decimal places. A study of 25 online jewelry retailers was done to find the statistical relationship between the price yyin dollars of a diamond ring and the weight xxin carats of the diamond. Based on this data the following least-squares regression line was found: y^=−6047.75+11975.14x What is the predicted price of diamond ring a 2.2 carat diamond using this regression line. Round your answer to two decimal places. A study of 25 online jewelry retailers was done to find the statistical relationship between the price yy in dollars of a diamond ring and the weight xx in carats of the diamond. Based on this data the following least-squares regression line was found: y^=−6047.75+11975.14x One online retailer sells a 3.00 carat diamond ring for 28,999…
The mean measured verbal IQ (IQV) score of a random sample of 20 children was 86.9 with a standard deviation of 18.5. The mean measured performance IQ score (IQP) of a random sample of 20 children was 101.8 with a standard deviation of 20.0. Using the Critical Value method and alpha = 0.005 to test the claim that the mean IQV is less than the mean IQP. Assume the population variances are not equal (so use unpooled). Step 4a: Find the test statistic. Round to 2 decimal places.
The tensile strength of steel bars produced by a manufacturer has a mean 30 MPa and the [10] standard deviation of 1.5MPa. By a new technique in the manufacturing process, it is claimed that the tensile strength can be improved. To test this claim, a sample of 50 steel bars is tested and it is found that the mean tensile strength is 30.5MPa. Can we support the claim at 0.01 level of significance?
a) Soil has been improved to increase the strength of a ground. The average compressive strength of 61 samples before treatment is 45 kg / cm2 and the standard deviation is 6.75 kg / cm2; The average compressive strength of 56 samples after the improvement is 52.5 kg / cm2 and the standard deviation is 8 kg / cm2. Determine whether the improvement application changes the standard deviation of the soil strength or not at the 5% significance level (15 P). b) Find the confidence intervals at the 7% significance level of the mean compressive strength of the sample after improvement?
One method for straightening wire prior to coiling it to make a 6. (Hypothesis Test, 2 spring is called "roller straightening". Suppose that a sample of 30 wires is selected and each is tested to determine tensile strength (N/mm²). The resulting sample mean and sample standard deviation are 2175 and 35, respectively. It is known that the mean tensile strength for spring made using spinner straightening is 2148 N/mm². (1) What is the random variable X in this problem? What does the mean µ of X represent? (2) What null hypothesis and alternative hypothesis should be tested in order to determine if the mean tensile strength for the roller method is better than the mean tensile strength for spinner method? (3) Is this one-tailed or two-tailed test? (4) What test statistic should be used to test the hypotheses? Is a normality assumption of the population necessary? Why? (5) At the significance level a = 0.05, compute the rejection region (RR). (6) Compute the value of your test statistic…

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