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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- 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?In simple linear regression, at what value of the independent variable, X, will the 95% confidence interval for the average value of Y be narrowest? At what value will the 95% prediction interval for the value of Y for a sin gle new observation be narrowest?
- 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]
- Your local gas company is interested in estimating the average usage during the month of January. A random sample of 1280 households found the following results: X= 82 therms and s=28 therms. Conduct a test of hypothesis to determine if the average amount exceeds 80 therms. Use a=0.02.The price X (dollars per pound) and consumption y (in pounds per capita) of beef were samples for 10 randomly selected years. The following data should be used to answer the question that follows. n = 10 Ex = 36.19 Ix² = 134.17 2.9 < x s 6.2 Ey = 774.7 Iy² = 60739.23 Exy = 2832.21 Using this data, a student calculated SSy = 28.43 SSx = 3.2 SSy= 717. Calculate the %3D %3D value of the standard error or regression, Se , and enter you answer accurate to the nearest hundredth (2 decimal places).Two researchers conduct separate studies to test Ho: p=0.50 against H₂: p0.50, each with n = 400. Researcher A gets 219 observations in the category of interest, and p=219/400 = 0.5475. Researcher gets 221 in the category of interest, and p=221/400=0.5525. Complete parts (a) through (e) below. a. Determine the P-value for Researcher A. The z test statistic is 1.90. The P-value is (Round to three decimal places as needed.) G
- Two researchers conduct separate studies to test Ho: p=0.50 against H₂: p0.50, each with n = 400. Researcher A gets 219 observations in the category of interest, and p=219/400 = 0.5475. Researcher gets 221 in the category of interest, and p=221/400=0.5525. Complete parts (a) through (e) below. a. Determine the P-value for Researcher A. The z test statistic is 1.90. The P-value is 0.057. (Round to three decimal places as needed.) b. Determine the P-value for Researcher B. The z test statistic is 2.10. The P-value is (Round to three decimal places as needed.) CThe 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 dentist wanted to determine if a relationship existed between childhood fluoride exposure and cavities. She took a sample of adults in her practice and counted how many cavities each person had in his or her permanent teeth. She also determined how many years of childhood each person was exposed to tap water with fluoride. The minimum value on this variable was 0 and the maximum was 18. Using the data below, an alpha of .05 and a two-tailed test, was there a significant relationship? Years of fluoride Number of cavities 0 10 18 1 2 7 12 3 3 4 10 5 M = 7.5s =6.98 M = 5.00s = 3.16