A manufacturer claims that the resistance of components produced is exactly 7:5 2 quality control specialist carries out checks on this claim and on one production run, too random sample of 10 components and measured their resistance. The values obtained are. 7-65 7-60 7.65 7-70 7-55 7:55 7-40 7.40 7-50 7.50 (a) What conclusions will the quality control specialist make about the manufacturer's claim? (b) With what level of confidence will the claim be made?
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- B6. Pinan Insurance Company wants to study the relationship between the amount of fire damage and the distance between the burning house and the nearest fire station. This information will be used in setting rates for insurance coverage. For a sample of 30 claims for the last year, the director of the actuarial department determined the distance from the fire station (x) and the amount of fire damage, in thousands of dollars (y). The MegaStat output is reported below. ANOVA table Source Regression Residual Total Regression output Variables Intercept Distance-X Answer the following questions. SS 1,864.5782 1,344.4934 3,209.07 Coefficients 12.3601 4.7956 df 1 28 29 MS 1,864.5782 48.0176 Std. Error 3.2915 0.7696 c) Determine and interpret the coefficient of determination. F 38.83 t(df=28) 3.755 6.231 d) Determine the correlation coefficient. Interpret its value. How did you determine the sign of the correlation coefficient?B6. Pinan Insurance Company wants to study the relationship between the amount of fire damage and the distance between the burning house and the nearest fire station. This information will be used in setting rates for insurance coverage. For a sample of 30 claims for the last year, the director of the actuarial department determined the distance from the fire station (x) and the amount of fire damage, in thousands of dollars (y). The MegaStat output is reported below. ANOVA table Source Regression Residual Total Regression output Variables Intercept Distance-X Answer the following questions. SS 1,864.5782 1,344.4934 3,209.07 Coefficients 12.3601 4.7956 df 1 28 29 MS 1,864.5782 48.0176 Std. Error 3.2915 0.7696 F 38.83 t(df=28) 3.755 6.231 a) Write out the regression equation. Is there a direct or indirect relationship between the distance from the fire station and the amount of fire damage? b) How much damage would you estimate for a fire 5 miles from the nearest fire station?17:3. A manufacturer claimed that at least 95% of the equipment which he supplied to a factory conformed to specifications. An examination of a sample of 200 pieces of equipment revealed that 18 were faulty. Test this claim at a significance level of (i) 05; (ii) ·01.
- Imagine we are taking measurements from the height of mature shrubs. We are interested in seeing whether the shrubs we observe in a particular region differ from those we have observed elsewhere, which we measured as having a median height of 1.65 m. We measure 100 plants and identify that 21 have a height less than 1.65 m (a) What are the hypotheses I would use to test whether the typical height in the region of interest is different to the broader population? (b) If H0 is true, what is the sampling distribution of the number of trees smaller than 1.65 m? (c) Construct a 95% CI for the proportion smaller than the median. (d) Determine the p-value for the same hypotheses, and use this to do a hypothesis test with α = 0.05.2. "It is claimed that a car is driven on the average less than 18100 kilometers per year with a population standard deviation of 2500 kilometers. A company wants to test if their current car model is on par with this average. To test this, a random sample of 59 cars from the company were tested. Suppose you are an analyst of the company, would you suggest to make improvements in your car design if the random sample showed an average of 18500 kilometers? Use a 0.01 level of significance."a. There is no sufficient data to make a sound conclusion.b. I would recommend an improvement to the car design to improve performance.c. I will assume that the cars are on par with the average and recommend to do nothing.d. I will be certain that there is no need to improve the car design based on the result.Q.1 An Electronic equipment used for the analysis and storage of the data in an industry has three identical input devices/ports. Different components of the electronic equipment are connected to each other as shown in Figure Q.1. Assume the following estimated reliability values of the components as shown in Table Q.1. Calculate the reliability of the electronic equipment operating successfully with at least one input device/port for 1000 hours? Also, estimate Mean Time to Failure (MTTF) for the electronic equipment for 1000 hrs. Table Q.1 Component Failure rate (2) x 10°, per hr Input device/Port Storage drive Central Processing Unit (CPU) Manual Key Pad Monitor/screen to display results 45 35 7 5 10 Input device 1 Monitor/ Storage device Manual Input device 2 CPU Кeурad screen Input Figure Q.1 device 3
- 2. A manufacturer of construction materials claims that their structural steel rods have a mean tensile strength of 500Mpa. We test a sample of 9 of the rods for their tensile strength (in MPa) and record the results below. 494 491 477 485 493 507 474 493 508 From our sample, is there evidence to suggest that the true mean tensile strength of the rods is not 500 Mpa? Perform the appropriate hypothesis test. (a) Using the correct notation, define the parameter of interest. Then, state the null and alternative hypotheses for this study in terms of the parameter. (b) Specify (with justification) the test statistic and state its distribution (Z or T, and degrees of freedom, if needed) it follows. (c) Compute the observed value of the test statistic. (d) Compute the p-value or provide a range of appropriate values for the p-value. (e) Using the p-value, determine the level of evidence against Ho. In a plain English sentence, state a conclusion for the study. 22) In a random sample 765 adults in Jordan, 322 say they could not cover a 300 JD unexpected expense without borrowing money or going into debt. What population is under consideration in the data set? b. What parameter is being estimated? What is the point estimate for the parameter? d. What is the name of the statistic can we use to measure the uncertainty of the point а. с. estimate? e. Compute the value from part (d) for this context. f. A news analyst thinks the value is actually 50%. Should the news analyst be surprised by the data? g. Suppose the true population value was found to be 40%. If we use this proportion to recompute the value in part (e) using p = 0.4 instead of p, does the resulting value change much?5. The burning rates of two different solid-fuel propellants used in air crew escape systems are being studied. It is known that both propellants have approximately the same standard deviation of burning rate; that is, o1 =02 = 3 centimeters per second. Two random samples of n1 = 20 and n2 = 20 specimens are tested; the sample mean burning rates are x1 = 18 centimeters per second and x2 = 24 centimeters %3D %3D per second. 5.1. Test the hypothesis that both propellants have the same mean burning rate. Use a=0.05. What is the P-value? 5.2. Construct a 95% confidence interval on the difference in means µ1 -u2. What is the practical meaning of this interval?
- Independent random samples of business and economics faculty were asked to respond on a scale from 1 (strongly disagree) to 4 (strongly agree) to this statement: The threat and actuality of takeovers of publicly held companies provide discipline for boards and managers to maximize the value of the company to shareholders. For a sample of 202 business faculty, the mean response was 2.83 and the sample standard deviation was 0.89. For a sample of 291 economics faculty, the mean response was 3.00 and the sample standard deviation was 0.67. Test the null hypothesis that the population means are equal against the alternative that the mean is higher for economics faculty.1. The normality of a solution of sodium hydroxide as determined by an ‘analyst’ by six different titrations are found to be 0.5018, 0.5047, 0.5062, 0.5039, 0.5056 and 0.5038. Calculate the mean, median, average deviation, standard deviation and coefficient of variation 2. If the mean of 12 determinations = 9.59, and the true value = 9.03, find out whether or not this result is significant provided the standard deviation(s) is 0.16. Use student t-test to determine the following: a. P values for 10%, 5% and 1% b. Is the method used reliable?1. Let μ denote the true average level of radioactivity of the water in a nuclear plant. Five (5) picocuries per liter is considered the dividing line between safe and unsafe water. a. State the null and alternate hypothesis you would test if you worked at the plant andexplain why you chose your alternate hypothesis.b. In the context of this situation, describe what happens if there is a type I error and type II error.