A manufacturing company developed a new type of hollow block that has a mean compressive strength of 8 kilograms with a standard deviation of 0.5 kilogram. A random sample of 50 Iblocks is tested and found to have a mean compressive strength of 7.8 kilograms. Use a 0.01 level of significance. Which of the following best contrádicts the null hypothesis, u = 8 The null hypothesis is:
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- 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…A high school principal was concerned about the time his students were spending on home work in a week He randomly selected 50 students and found that mean time on home work was 18.50. Assume that the population standard deviation was 10.2 hrs. Use a = 0.10 to test his claims that his students spend significantly less that 20 hours in a week. In this case, null hypothesis Ho is Ομ > 20 Ομ 20 Ομ < 20 μ<The supervisor of a production line believes that the average time to assemble an electronic component is 14 minutes. Assume that assembly time is normally distributed with a standard deviation of 3.4 minutes. The supervisor times the assembly of 14 components, and finds that the average time for completion was 11.6 minutes. (H0: μ=14μ=14 and H1=μ≠14μ≠14) What is the z-value for a two-sided test of hypothesis for a population mean when the probability of rejecting a true null hypothesis is equal to 0.05?
- 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 axial load of an aluminum can is the maximum weight the sides can support before giving way. A soft drink manufacturer is testing aluminum cansthinner. A sample of 77 of these cans provided an average axial load equal to 48.72pounds. It is known that currently used cans have an average load of 48 pounds and astandard deviation of 23.23 pounds. Assuming the manufacturer wants to test whether the axial loadaverage of thinner cans is 48 against the hypothesis that average axial load of thinner cansfines is less than 48, tick the alternative corresponding to the p-value for the test. (a) 0.1968(b) 0.3936(c) 0.6064(d) 0.3503(e) 0.0890The braking ability was compared for two car models. Random samples of two cars were selected. The first random sample of size 64 cars yield a mean of 36 and a standard deviation of 8. The second sample of size 64 yield a sample mean of 33 and a standard deviation of 8. Do the data provide sufficient evidence to indicate a difference between the mean stopping distances for the two models? Use Alpha= 0.01. Ho: µ1 – µ2 = 0 vs. Ha: µ1 – µ2 + 0 .p-value = 0.0017. Reject Ho Но: Д, — м2 — 0 vs. Ha:M1 — M2 + 0. p-value — 0.034. Ассеpt Ho O Ho:µ1 – Hz Но: И — 2 — 0 vs. Ha:M, — нz + 0. p-value —D 0.0017. Ассept Ho Ho: H1 – U2 = 0 vs. Ha: µ1 – µ2 + 0. p-value = 0.034. Reject Ho
- At a water bottling facility, a technician is testing a bottle filling machine that is supposed to deliver 500 ml of water, and in the past the standard deviation of the population of bottles has be 7.5 ml. The technician dispenses 39 samples of water and determines the volumes have a mean of 498.3 ml. The technician wants to perform a hypothesis test at (alpha) = 0.05 level to determine whether the machine is not dispensing 500 ml, and is thus out of calibration. Hypothesis Statement: Test Value(s): So, we ____ the null hypothesis because ______. There ______ enough evidence to support the claim that the machine mean volume differs from 500 ml and is out of calibration.A sample of 12 concrete specimens from supplier A were tested for their compressive strength. The results gave an average of 85 MPa and a standard deviation of 4 MPa. From supplier B, 10 specimens were similarly tested and gave an average compressive strength of 81 MPa and a standard deviation of 5 MPa. (a) Using procedures of Hypothesis Testing, can we conclude at the 0.05 level of significance that the compressive strength of concrete from A exceeds that from B by more than 2 MPa? Assume the populations to be approximately normal with equal variances. (b) Is the assumption of equal variances in (a) justifiable at an a = 0.10?