Based on a large sample of capacitors of a certain type, a 95% confidence interval for the mean capacitance, in μF, was computed to be (0.217, 0.257). Find a 90% confidence interval for the mean capacitance of this type of capacitor. (Round the final answers to three decimal places.)
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![Based on a large sample of capacitors of a certain type, a 95% confidence interval for the mean capacitance, in μF, was computed to
be (0.217, 0.257). Find a 90% confidence interval for the mean capacitance of this type of capacitor. (Round the final answers to three
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- The scores of a random sample of 100 high school students on a standardized mathematics test in a certain school gave a mean of 78 and a standard deviation of 20.Find the 95% confidence interval estimate for the true average score in mathematics in this standardized test. Formula: E=zα/2(σ/√n)A series of tests of fire prevention sprinkler systems that use a foaming agent to quell the fire were performed to determine how long it took (in seconds) for the sprinklers to be activated after the detection of a fire by the system. The system has been designed so that the true average activation time is supposed to be at most 25 seconds. Do the data strongly indicate that the design specifications have not been met? The data for the test are given below: 27 41 22 27 23 35 30 33 24 27 28 22 24A researcher noticed that today's adolescents seem to have higher rates of social anxiety than those of generations past. In 1990, the average level of social anxiety in adolescents was μ = 15.5. The researcher collects data by sampling 100 adolescent students from the tristate area and records their level of anxiety. Testing at an alpha level of a = .05, what will the researcher conclude about today's adolescents? a.) Step 1: State the Hypotheses H₂: H₁: b.) Step 2: Determine the critical region and draw it on the distribution above: df = c.) Step 3: Calculate the test statistic the sample mean is 16.5 and SS = 0.25 M= SM= tobs d.) Step 4: Make a decision. Circle one: Reject Null (Ho) or e.) State your conclusions about the research scenario in sentence form: tcritical = 72²= Fail to Reject Null (Ho) f.) Calculate an effect size in terms of the variance account for (2)? Do you characterize it as being small, medium or large?
- A pilot study was performed to investigate the effect of temperature, x (in degree Fahrenheit) on the electrical power consumed, y (in Watt) by an automotive factory. Other factors were kept constant and the data were collected from the study. The summary of the data are given as follows: n = 8, 2x = 401, 2301, x? = 22495 2y? = 666509, Σ > xy = 118652. %3D Compute the equation of the least squares regression line of y on x. Interpret the equation obtained in part (i). Predict the power consumption for a temperature of 65°F. (i) (ii) (iii) (iv) Compute the coefficient of determination and explain.According to a report from the United States Environmental Protection Agency, burning one gallon of gasoline typically emits about 8.9 kg of CO2. A fuel company wants to test a new type of gasoline designed to have lower CO2 emissions. Their hypotheses are Ho : µ = 8.9 kg and H, : µ < 8.9 kg. where u is the mean amount of CO, emitted by burning one gallon of this new gasoline. Suppose that Ho is actually true. Which situation below would have the lowest probability of a Type I error? Choose 1 answer: n = 20 and a = 0.01 n = 50 and a = 0.05 n = 75 and a = 0.10Given the supplied information, interpret the results. Be sure to (1) tell what was done, (2) present some facts, (3) interpret the results, and (4) make a suggestion for future research. (Assume the test is two-tailed and α = .05). A statistics professor has compared the systolic blood pressure of her class (N = 24) (M = 138, s = 16) to blood pressure in the general population (μ = 120) to see if taking statistics is related to higher or lower blood pressure. She found: • tcv = 2.069 • t = 5.50 • d = 1.13 • r2 = 57% • 95% CIDiff [11.23, 24.77]
- The College Board states that the students spend an average of $1200each year on textbooks. The Dean of a university believes it’s not the average at hisschool. He samples 51 students and finds they have an average cost of $1260 with astandard deviation of $175. What critical value is needed for this test at alpha=0.05? a. Z = +/- 1.65b. Z = +/- 2.44c. T=+/- 1.676d. T=+/- 2.009A standard method (based on thousands of measurements) for CO2 analysis has a standard deviation of 1 ppm. A modified method has a standard deviation of 0.5 ppm, for 20 degrees of freedom? With 95% confidence, is this alternative method more precise?Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 136 to 190 cm and weights of 39 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yiel x= 167.51 cm, y = 81.36 kg,r= 0.232, P-value = 0.020, and y = - 103+ 1.13x. Find the best predicted value of y (weight) given an adult male who is 153 cm tall. Use a 0.01 significance level. The best predicted value of y for an adult male who is 153 cm tall is kg. (Round to two decimal places as needed.)
- Question 1 {0 decimal places } Find the value of the sample mean.A random sample of CO2 levels in a school has a sample mean of x¯=598.4 ppm and sample standard deviation of s=86.7 ppm. Use the Empirical Rule to determine the approximate percentage of CO2 levels that lie between 338.3 and 858.5 ppm.Arsenic-based additives in chicken feed have been banned by the European Union. Ifa restaurant chain finds significant evidence that the mean arsenic level of theirchickens is above 80 ppb (parts per billion), the chain will stop using that supplier ofchicken meat. The hypotheses are: H 0 : µ = 80H 1 : µ > 80 where µ represents the mean arsenic level in all chicken meat from that supplier.Samples from two different suppliers are analyzed, and the resulting p-values aregiven: Sample from Supplier A: p-value is 0.0003Sample from Supplier B: p-value is 0.3500 a) Interpret each p-value in terms of the probability of the results happening byrandom chance. b) Which p-value shows stronger evidence for the alternative hypothesis? c) Which supplier, A or B, should the chain get chickens from in order to avoid toohigh a level of arsenic?
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