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…The 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 HoA 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?
- The average size of a farm in one county is 162 acres with a standard deviation of 38 acres. The average size of a farm in a second county is 182 acres with a standard deviation of 16 acres. Assume the data were obtained from two samples that had 30 farms each. Can it be concluded that the average size of the farms in the two counties is different? (Let α = 0.05) First , choose which hypothesis statements is correct. T-stat = Round to 2 decimal places. P-value = Decision: Type Retain Ho or Reject Hohe average American consumes 96 liters of alcohol per year. Does the average college student consume more alcohol per year? A researcher surveyed 13 randomly selected college students and found that they averaged 104.4 liters of alcohol consumed per year with a standard deviation of 18 liters. What can be concluded at the the αα = 0.10 level of significance? For this study, we should use The null and alternative hypotheses would be: H0:H0: H1:H1: The test statistic = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is αα Based on this, we should the null hypothesis. Thus, the final conclusion is that ... The data suggest the population mean is not significantly more than 96 at αα = 0.10, so there is statistically insignificant evidence to conclude that the population mean amount of alcohol consumed by college students is equal to 96 liters per year. The…a consumer group claims that the mean acceleration time from 0 to 60 miles per hour for a sedan is 6.3 seconds. A random sample of 33 sedans has a mean acceleration time from 0 to 60 miles per hour is 7.2 seconds. Assume that the population standard deviation is 2.5 seconds.At alpha = 0.05, can you reject the claim?
- A random sample of 23 bags of apples (marked as 10 pounds each) received by a large grocery chain tested out as having a mean of 9.2 pounds with a variance of 2.56 pounds. Test whether the true mean of all bags is under 10 pounds. Set up hypotheses. Perform the appropriate test by showing your formula. Interpret the results using a Type I (alpha) error of .05. Also provide the p value here. Also construct a 95% confidence interval around your sample mean (X bar) that should contain the true mean (mu). Also interpret this interval.Currently patrons at the library speak at an average of 65 decibels. Will this average increase after the installation of a new computer plug in station? After the plug in station was built, the librarian randomly recorded 52 people speaking at the library. Their average decibel level was 70.5 and their standard deviation was 15. What can be concluded at the the αα = 0.01 level of significance? For this study, we should use The null and alternative hypotheses would be: H0:H0: H1:H1: The test statistic = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is αα Based on this, we should the null hypothesis.The average weight of a Fuji apple weighs 0.5 pounds. Your local grocery store claims that its Fuji apples on average are larger (heavier) than typical Fuji apples. To verify the grocery store’s claim, you decided to implement a hypothesis test. You bought 12 Fuji apples from the store and found that the mean weight is 0.65 pounds with a standard deviation of 0.1 pounds. What is the P-value? Assume that alpha = 0.05. A. P-value < 0.0005 B. 0.0005 < P-value < 0.001 C. 0.001 < P-value < 0.0025 D. 0.0025 < P-value < 0.005
- When 40 people used the Weight Watchers dies for one year, their mean weight loss was 3.0 lb and the standard deviation was 4.9 lb. Use a 0.01 significance level to test the claim that the mean weight loss is greater than 0. (Show the solution) A. The null hypothesis is i. The mean weight loss is equal to 0. ii. The mean weight loss is not equal to 0. iii. The mean weight loss is greater than 0. iv. The mean weight loss is less than 0. B. The computed t-test statistic is i. 4.468 ii. 4.977 iii. 3.872 iv. 3.391 C. The critical/tabular t-test statistic is i. 2.426 ii. 1.684 iii. 1.685 iv. 2.423 D. Decision rule: i. Do not reject the null hypothesis. ii. Reject the null hypothesis. E. The final conclusion is i. The mean weight loss is not equal to 0 therefore Weight Watchers is effective. ii. The mean weight loss is less than 0 therefore Weight Watchers is not effective. iii. The mean weight loss is equal to 0 therefore Weight Watchers…It is claimed that an automobile is driven on the average more than 20,000 kilometers per year. To test this claim, a random sample of 100 automobile owners were asked to keep a record of the kilometers they travel. Would you agree with this claim if the random sample showed an average of 23,500 kilometers and std deviation of 3900 kilometers? Use α = 0.05. Use a P-value in your conclusion. Please make the solution detailed and clear.Beta company is manufacturing steel wire with an average tensile and strenght of 50 kilos. The laboratory tests 16 pieces and finds that the mean is 47 kilos and the standard deviation of is 15 kilos. Are the reuslts in accordance with the hypothesis that the population mean is 50 kilos.